HCF & LCM - Class 1 PDF

 ABHINAY MATHS CLASSES LCM & HCF 1. The LCM of two numbers is 864 and their HCF is 8. Four bells ring at intervals of 4, 6, 8 and 14 seconds. 144. If one numbe...

 ABHINAY MATHS CLASSES LCM & HCF 1. The LCM of two numbers is 864 and their HCF is 8. Four bells ring at intervals of 4, 6, 8 and 14 seconds. 144. If one number is 288, the other number is They start ringing simultaneously at 12.00 O' clock. nks la[;kvksa dk y-l- 864 rFkk e-l- 144 gSA ;fn mlesa At what time will they again ring simultaneously? ls ,d la[;k 288 gS] rks nwljh la[;k Kkr djsaA pkj ?kafV;k¡ 4] 6] 8 rFkk 14 lsd.M ds varjky ij (a) 576 (b) 1296 ctrh gS os 12 cts ,d lkFk ctuk vkjaHk djrh gS] rks (c) 432 (d) 144 iqu% fdrus cts os ,d lkFk ctsaxh\ 2. LCM of two numbers is 225 and their HCF is 5. If (a) 12 hrs. 2 min. 48 sec. one number is 25, the other number will be: (b) 12 hrs. 3 min. nks la[;kvksa dk y-l- 225 rFkk e-l- 5 gSA ;fn mlesa ls(c) 12 hrs. 3 min. 20 sec ,d la[;k 25 gS] rks nwljh la[;k Kkr djsaA (d) 12 hrs. 3 min. 44 sec. (a) 5 (b) 25 9. The product of the LCM and HCF of two numbers (c) 45 (d) 225 is 24. The difference of the two numbers is 2. Find 3. The LCM of two numbers is 30 and their HCF is 5. the numbers? One of the numbers is 10. The other is number will nks la[;kvksa ds y-l- rFkk e-l- dk xq.kuiQy 24 gSA mu be. la[;kvksa ds chp dk varj 2 gS] rks la[;k,¡ Kkr djsaA nks la[;kvksa dk y-l- 225 rFkk e-l- 5 gSA ;fn mlesa ls (a) 8 and 6 (b) 8 and 10 ,d la[;k 10 gS] rks nwljh la[;k Kkr djsaA (c) 2 and 4 (d) 6 and 4 (a) 5 (b) 25 10. The LCM of two numbers is 495 and their HCF is (c) 45 (d) 225 5. If the sum of the numbers is 100, then their 4. The HCF and LCM of two numbers are 13 and 455 difference is: nks la[;kvksa dk y-l- 495 rFkk e-l- 5 gSA ;fn mu respectively. If one of the numbers lies between 75 and 125, then that number is: la[;kvksa dk ;ksx 100 gS] rks mudk varj D;k gksxk\ nks la[;kvksa dk e-l- o y-l- Øe'k% 13 rFkk 455 gSA (a) 10 (b) 46 ;fn ,d la[;k 75 rFkk 125 ds chp gS] rks og la[;k (c) 70 (d) 90 D;k gS\ 11. Two numbers, both greater than 29, have HCF 29 (a) 78 (b) 91 and LCM 4147. Find sum of two numbers. (c) 104 (d) 117 29 ls cM+h nks la[;kvksa dk e-l- 29 rFkk y-l- 4147 5. The least number which when divided by 4, 6, 8, 12 gS] rks mu la[;kvksa dk ;ksx Kkr djsaA and 16 leaves a remainder of 2 in each case is: (a) 966 (b) 696 og U;wure la[;k D;k gS ftlesa 4] 6] 8] 12 rFkk 16 (c) 669 (d) 666 ls Hkkx nsus ij izR;sd fLFkfr esa 2 'ks"k cprk gS\ 12. The H.C.F. of two numbers is 8. Which one of the (a) 46 (b) 48 following can never be their L.C.M? (c) 50 (d) 56 nks la[;kvksa dk e-l- 8 gS] rks buesa ls dkSu ,d mudk 6. The least number, which when divided by 12, 15, 20 or 54 leaves a remainder of 4 in each case is : y-l- ugha gks ldrk gS\ og U;wure la[;k D;k gS] ftlesa 12] 15] 20 ;k 54 ls (a) 24 (b) 48 Hkkx nsus ij izR;sd fLFkfr esa 4 'ks"k cprk gS\ (c) 56 (d) 60 (a) 456 (b) 454 13. The LCM and HCF of the numbers 28 and 42 are in the ratio: (c) 540 (d) 544 7. The maximum number of students among whom nks la[;k,¡ 28 rFkk 42 ds y-l- rFkk e-l- dk vuqikr 1001 pens and 910 pencils can be distributed in such D;k gksxk\ a way that each student gets same number of pens (a) 6 : 1 (b) 2 : 3 and same number of pencil, is: (c) 3 : 2 (d) 7 : 2 Nk=kksa dh vfèkdre la[;k Kkr djsa ftuds chp14.1001The LCM of two numbers is 1820 and their HCF is dye rFkk 910 isaflyks dks bl rjg ck¡Vk tkrk gS fd 26. If one number is 130 then the other number is: izR;sd Nk=k dks cjkcj la[;k esa dye rFkk cjkcj la[;knks la[;kvksa dk y-l- 1820 rFkk e-l- 26 gSA ;fn ,d esa isafly izkIr gksrk gSA la[;k 130 gS] rks nwljh la[;k Kkr djsaA (a) 91 (b) 910 (a) 70 (b) 1690 (c) 1001 (d) 1911 (c) 364 (d) 1264 Contact No. : 9555202436, 9716761136 2 oDr cnyrk gS] fQj cnysxk A lkjk tgk¡ viuk gksxk AA A-7, Top Floor, Jai Building, Commercial Complex Near Chawla Restaurant, Dr Mukherjee Nagar, Delhi-110009  ABHINAY MATHS CLASSES 15. The LCM of two numbers is 1920 and their HCF is 22. The greatest number, Which when divides 989 and 16. If one of the number is 128, find the other number. 1327 leave remainders 5 and 7 respectively: nks la[;kvks dk y-l- 1920 gS rFkk e-l- 16 gSA ;fnog vfèkdre la[;k D;k ftlls 989 rFkk 1327 esa Hkkx ,d la[;k 128 gS] rks nwljh la[;k Kkr djsaA nsus ij Øe'k% 5 rFkk 7 'ks"k cprk gks\ (a) 204 (b) 240 (a) 8 (b) 16 (c) 260 (d) 320 (c) 24 (d) 32 16. The HCF of two number 12906 and 14818 is 478. 23. A milkman has 75 lt milk in one cane and 45 lt in Their LCM is : another, The maximum capacity of container which can measure milk of either container exact number : nks la[;k,¡ 12906 vkSj 14818 dk e-l- 478 gS] rks y-l- Kkr djsaA ,d nwèkokys ds ikl ,d dksu esa 75 yh- nwèk gS rFkk nwljs (a) 400086 (b) 200043 dsu esa 45 yh- nwèk gsA mlds ik=k dh vfèkdre {kerk (c) 600129 (d) 800172 D;k gksxh] tks nksuksa dsuksa ds nwèk dh ek=kk dks eki ld 17. Find the greatest number of five digits which when (a) 1 litre (b) 5 litre divided by 3, 5, 8, 12 leaves 2 as remainder. (c) 15 litre (d) 25 litre ik¡p vadksa dh vfèkdre la[;k Kkr djsa ftlesa 3]24. 5] 8] Two numbers are in the ratio 3 : 4. If their HCF is 4, then their LCM is: 12 ls Hkkx nsus ij 2 'ks"k cprk gSA nks la[;k,¡ 3%4 ds vuqikr esa gSA ;fn mudk e-l- 4 gS] (a) 99999 (b) 99948 rks mudk y-l- Kkr djsaA (c) 99962 (d) 99722 (a) 48 (b) 42 18. The least multiple of 13, which on dividing by 4, 5, 6, 7 and 8 leaves remainder 2 in each case is: (c) 36 (d) 24 13 dk og U;wure xq.kd D;k gS ftlesa 4] 5] 6] 725. rFkkFind the least multiple of 23, which when divided by 18, 21 and 24 leaves the remainder 7, 10 and 13 8 ls Hkkx nsus ij izR;sd fLFkfr esa 2 'ks"k cprk gS\ respectively. (a) 2520 (b) 842 23 dk U;wure xq.kd Kkr djsa] ftlesa 18] 21 rFkk 24 (c) 2522 (d) 840 ls Hkkx nsus ij Øe'k% 7] 10 rFkk 13 'ks"k cpsa\ 19. Find the largest number of four digits such that on (a) 3013 (b) 3024 dividing by 15, 18, 21 and 24 the remainders are (c) 3002 (d) 3036 11, 14, 17 and 20 respectively. 26. The HCF of two numbers is 16 and their LCM is pkj vadksa dh og vfèkdre la[;k Kkr djsa ftlesa 15] 160. If one of the number is 32, then the other 18] 21 rFkk 24 ls Hkkx nsus ij Øe'k% 11] 14] 17 rFkk number is: 20 'ks"k cprk gSA nks la[;k,¡ 3%4 ds vuqikr esa gSA ;fn mudk e-l- 4 gS] (a) 6557 (b) 7556 rks mudk y-l- Kkr djsaA (c) 5675 (d) 7664 (a) 48 (b) 80 1 (c) 96 (d) 112 20. 4 bells ring at intervals of 30 minutes, 1 hour, 1 2 27. The product of two number is 4107. If the HCF of the hour and 1 hour 45 minutes respectively. All the numbers is 37, the greater number is : bells ring simultaneously at 12 noon. They will again nks la[;kvks dk xq.kuiQy 4107 gSA ;fn mudk e-l- 37 ring simultaneously at: gS] rks cM+h la[;k D;k gS\ 1 4 ?kafV;k¡ Øe'k% 30 feuV]1 1 ?kaVk] ?kaVk rFkk 1 ?kaVk 45(a) 185 (b) 111 2 (c) 107 (d) 101 feuV ds varjky ij ctrh gSA lHkh ?kafV;k¡ ,d lkFk 12 cts 28. The least perfect square, which is divisible by each nksigj esa cth gks] rks os iqu% ,d lkFk dc ctsaxh\ of 21, 36 and 66 is: (a) 12 mid night (b) 3 a.m. og U;wure oxZ D;k gS tks 21] 36 rFkk 66 izR;sd ls (c) 6 a.m. (d) 9 p.m. iw.kZr% foHkkftr gS\ 21. Four bells ring at the intervals of 5, 6, 8 and 9 (a) 214344 (b) 214434 seconds. All the bells ring simultaneously at some (c) 213444 (d) 231444 time. They will again ring simultaneously after. 29. The least number, which when divided by 4, 5 and pkj ?kafV;k¡ 5] 6] 8 rFkk 9 lsds.M ds varjky ij ctrh 6 leaves remainder 1, 2 and 3 respectively, is: gSA lHkh ?kafV;k¡ fdlh le; ,d lkFk ctrh gSa rks os iqu% og U;wure la[;k D;k gS] ftlesa 4] 5 rFkk 6 ls Hkkx nsus ,d lkFk fdrus le; ckn ctsxh\ ij Øe'k% 1] 2 rFkk 3 'ks"k cprk gS\ (a) 6 minutes (b) 12 minutes (a) 57 (b) 59 (c) 18 minutes (d) 24 minutes (c) 61 (d) 63 Contact No. : 9555202436, 9716761136 3 oDr cnyrk gS] fQj cnysxk A lkjk tgk¡ viuk gksxk AA A-7, Top Floor, Jai Building, Commercial Complex Near Chawla Restaurant, Dr Mukherjee Nagar, Delhi-110009  ABHINAY MATHS CLASSES 30. Let the least number of six digits which when (a) 30, 40 (b) 40, 32 divided by 4, 6, 10, 15 leaves in each case same (c) 24, 30 (d) 36, 20 remainder 2 be N. The sum of digits in N is: 37. Three numbers which are co-prime to one another eku fy;k tk, fd 6 vadks dh og U;wure la[;kN gS] are such that the product of the first two is 551 and ftlesa 4] 6] 10 rFkk 15 ls Hkkx nsus ij izR;sd fLFkfrthat esaof the last two is 1073. The sum of the three 2 'ks"k cprk gS]Nrks la[;k ds vadksa dk ;ksx Kkr djsa\ numbers is: (a) 3 (b) 5 rhu la[;k,¡] tks ,d nwljs dh lgvHkkT; la[;k,¡ gSaA (c) 4 (d) 6 igyh nks la[;kvksa dk xq.kuiQy 551 rFkk vafre nks 31. Which is the least number which when doubled will la[;kvksa dk xq.kuiQy 1073 gS] rks rhuksa la[;kvksa dk be exactly divisible by 12, 18, 21 and 30? ;ksx Kkr djsa\ og U;wure la[;k D;k gS] ftls nksxquk djus ij og 12](a) 75 (b) 81 18] 21 rFkk 30 ls iw.kZr% foHkkftr gks tkrh gS\ (c) 85 (d) 89 (a) 2520 (b) 1260 38. HCF and LCM of two numbers are 7 and 140 (c) 630 (d) 196 respectively. If the numbers are between 20 and 45, 32. The smallest square number divisible by 10, 16 and the sum of the numbers is: 24 is: nks la[;kvksa dk e- l- o y- l- Øe'k% 7 rFkk 140 gSA og U;wure oxZ dh la[;k D;k gS] tks 10] 16 rFkk 24;fn la[;k,¡ 20 rFkk 45 ds chp esa gS] rks la[;kvksa dk ls iw.kZr% foHkkftr gS\ ;ksx Kkr djsa\ (a) 900 (b) 1600 (a) 70 (b) 77 (c) 2500 (d) 3600 (c) 63 (d) 56 33. From a point on a circular track 5 km long A, B and 39. The HCF of two numbers is 15 and their LCM is C started running in the same direction at the same 300. If one of the number is 60, the other is: 1 time with speed of 2 km per hour, 3 km per hour nks la[;kvksa dk e-l- rFkk y- l- Øe'k% 15 rFkk 300 2 gSA ;fn ,d la[;k 60 gS] rks nwljh la[;k Kkr djsa\ and 2 km per hour respectively. Then on the starting point all three will meet again after. (a) 50 (b) 75 (c) 65 (d) 100 5 fd-eh- dh nwjh okys ,d o`ÙkkdkjA, iFkB rFkk ij 40. The HCF of two numbers is 23 and the other two C ,d gh LFkku ls ,d gh fn'kk esa] ,d gh le; Øe'k% factors of their LCM are 13 and 14. The larger of 1 2 fdeh@?kaVk] 3 fdeh@?kaVk 2 fdeh@?kaVk rFkk izfr ?kaVsthe two numbers is: 2 nks la[;kvksa dk e- l- 23 gS rFkk muds y- l- ds vU; nks dh xfr ls nkSM+uk vkjaHk djrs gSa] rks vkjafHkd fcanq ij os iqu% fdruh nsj ckn feysaxs\ xq.ku[k.M 13 rFkk 14 gSa] rks mu la[;kvksa esa ls cM+h la[;k D;k gS\ (a) 30 hours (b) 6 hours (a) 276 (b) 299 (c) 10 hours (d) 15 hours (c) 345 (d) 322 34. What is the least number of square tiles required to pave the floor of a room 12 m 17 cm long and 9m, 41. If the students of a class can be grouped exactly 2cm broad ? into 6 or 8 or 10, then the minimum number of student in the class must be. 15 eh- 17 lseh- yEcs rFkk 9 eh 2 lseh- pkSM+s iQ'kZ ij fcNkus ds fy;s de ls de fdrus oxZdkj VkbZyksa dh ;fn ,d d{kk ds Nk=kksa dh 6 ;k 8 ;k 10 ds lewgksa esa t:jr gksxh\ ck¡Vk tkrk gS] rks d{kk esa U;wure fdrus Nk=k gS\ (a) 840 (b) 841 (a) 60 (b) 120 (c) 820 (d) 814 (c) 180 (d) 240 35. If the ratio of the two numbers is 2 : 3 and their 42. The least number which when divided by 4, 6, 8 LCM is 54, then the sum of the two number is: and 9 leave zero remainder in each case and when divided by 13 leaves a remainder of 7 is: ;fn nks la[;kvksa dk vuqikr 2 % 3 gS rFkk mudk y- l- 54 gS] rks la[;k,¡ Kkr djsa\ og U;wure la[;k Kkr djsa ftlesa 4] 6] 8 rFkk 9 ls (a) 5 (b) 15 Hkkx nsus ij izR;sd fLFkfr esa 'kwU; 'ks"k cprk gS vkSj 13 (c) 45 (d) 270 ls Hkkx nsus ij 7 'ks"k cprk gS\ 36. (a) 144 The ratio of two numbers is 4 : 5 and their LCM is (b) 72 120. The numbers are (c) 36 (d) 85 nks la[;kvksa dk vuqikr 4 % 5 gS] rFkk mudk43. y-l- 120 The number nearest to 10000, which is exactly divisible by each of 3, 4, 5, 6, 7 and 8, is : gS] rks la[;k,¡ Kkr djsaA Contact No. : 9555202436, 9716761136 4 oDr cnyrk gS] fQj cnysxk A lkjk tgk¡ viuk gksxk AA A-7, Top Floor, Jai Building, Commercial Complex Near Chawla Restaurant, Dr Mukherjee Nagar, Delhi-110009  ABHINAY MATHS CLASSES 10]000 fudVre og la[;k D;k gS] tks 3] 4] 5] 6] 7 ls Hkkx nsus ij 3 'ks"k cprk gS ysfdu 9 ls Hkkx nsus ij rFkk 8 ls iw.kZr% foHkkftr gks\ dksbZ 'ks"k ugha cprk gS\ (a) 9240 (b) 10080 (a) 123 (b) 603 (c) 9996 (d) 10000 (c) 723 (d) 243 44. Let N be the greatest number that will divide 1305, 51. What is the least number which when divided by 4665 and 6905 leaving the same remainder in each the number 3, 5, 6, 8, 10 and 12 leaves in each case case. a remainder 2 but when divided by 22 leaves no remainder? eku fy;k tk, fd N og vfèkdre la[;k gS] ftlls og U;wure la[;k D;k gS ftlesa 3] 5] 6] 8] 10 rFkk 12 1305] 4665 rFkk 6905 dks Hkkx nsus ij izR;sd fLFkfr ls Hkkx nsus ij izR;sd fLFkfr esa 2 'ks"k cprk gS ysfdu esa cjkcj 'ks"k cprk gS] N la[;k rks ds vadksa dk ;ksx 22 ls Hkkx nsus ij dksbZ 'ks"k ugha cprk\ Kkr djsa\ (a) 312 (b) 242 (a) 4 (b) 5 (c) 1562 (d) 1586 (c) 6 (d) 8 52. What is the greatest number that will divide 307 45. The sum of two numbers is 36 and their HCF is 4. and 330 leaving remainder 3 and 7 respectively ? How many pairs of such number are possible? og vfèkd la[;k D;k gS ftlls 307 rFkk 330 dks foHkkftr nks la[;kvksa dk ;ksx 36 gS rFkk mudk e-l- 4 gS] rks bl djus ij Øe'k% 3 vkSj 7 'ks"k cprk gS\ rjg dh la[;kvksa ds laHkkfor tksM+ksa dh la[;k D;k gksxh\ (a) 19 (b) 16 (a) 1 (b) 2 (c) 17 (d) 23 (c) 3 (d) 4 53. The sum of the HCF and LCM of two number is 680 and the LCM is 84 times the HCF. If one of the 46. The greatest number, that divides 122 and 243 number is 56. The other is: leaving respectively 2 and 3 as remainders is: nks la[;kvksa ds e-l- rFkk y-l- dk ;ksx 680 gS] mudk og vfèkdre la[;k Kkr djsa ftlesa 122 rFkk 243 Hkkx y-l-] e-l- dk 84 xq.kk gSA ;fn ,d la[;k 56 gS] rks nsus ij Øe'k% 2 rFkk 3 'ks"k cprk gS\ nwljh la[;k Kkr djsa\ (a) 12 (b) 24 (a) 84 (b) 12 (c) 30 (d) 120 (c) 8 (d) 96 47. The HCF and LCM of two 2-digit number are 16 54. The LCM of two numbers is 20 times their HCF. and 480 respectively. The numbers are : The sum of HCF and LCM is 2520. IF one of the number 480, the other number is: nks vadks dh nks la[;kvksa dk e-l- o y-l- Øe'k% 16 rFkk 480 gS] rks la[;k,¡ Kkr djsa\ nks la[;kvksa dk y-l- muds e-l- dk 20 xq.kk gS] muds e-l- rFkk y-l- dk ;ksx 2520 gSA ;fn ,d la[;k 480 (a) 40, 48 (b) 60, 72 gS] rks nwljh la[;k Kkr djsa\ (c) 64, 80 (d) 80, 96 (a) 400 (b) 480 48. The smallest number, which when divided by 12 (c) 520 (d) 600 and 16 leaves remainder 5 and 9 respectively, is: 55. The largest 4-digit number exactly divisible by each og U;wure la[;k D;k gS ftlesa 12 rFkk 16 ls Hkkx nsus of 12, 15, 18 and 27 is: ij Øe'k% 5 rFkk 9 'ks"k cprk gS\ 4 vadks dh og vfèkdre la[;k D;k gS] tks 12] 15] 18 (a) 55 (b) 41 rFkk 27 ls iw.kZr% foHkkftr gS\ (c) 39 (d) 29 (a) 9690 (b) 9720 49. A number which when divided by 10 leaves a (c) 9930 (d) 9960 remainder of 9, when divided by 9 leaves a 56. Which greatest number will divide 3026 and 5053 remainder of 8, and when divided by 8 leaves a leaving remainders 11 and 13 respectively? remainder of 7, is: og vfèkdre la[;k D;k gS ftlls 3026 rFkk 5053 dh ,d la[;k esa tc 10 ls Hkkx fn;k tkrk gS] rks 9 'ks"k cprk foHkkftr djus ij Øe'k% 11 rFkk 13 'ks"k cprk gS\ gS] tc 9 ls Hkkx fn;k tkrk gS] rks 8 'ks"k cprk gS vkSj(a)8 19 (b) 30 ls Hkkx fn;k tkrk gS] rks 7 'ks"k cprk gS] rks la[;k Kkr (c) djsa\17 (d) 45 (a) 1539 (b) 539 57. The greatest number, by which 1657 and 2037 are divided to give remainders 6 and 5 respectively, is: (c) 359 (d) 1359 50. What is the smallest number which leaves remainder og vfèkdre la[;k D;k gS ftlls 1657 rFkk 2037 dks 3 when divided by any of the numbers 5, 6 or 8 but foHkkftr djus ij Øe'k% 6 rFkk 5 'ks"k cprk gS\ leaves no remainder when it is divide by 9 ? (a) 127 (b) 133 og U;wure la[;k D;k gS ftlesa 5] 6 ;k 8 fdlh la[;k (c) 235 (d) 305 Contact No. : 9555202436, 9716761136 5 oDr cnyrk gS] fQj cnysxk A lkjk tgk¡ viuk gksxk AA A-7, Top Floor, Jai Building, Commercial Complex Near Chawla Restaurant, Dr Mukherjee Nagar, Delhi-110009  ABHINAY MATHS CLASSES 58. The product of two numbers is 1280 and their HCF 1 is 8. The LCM of the number will be: nks la[;kvksa dk ;ksx 45 gSA mudk varj ;ksx gS] dk 9 nks la[;kvksa dk xq.kuiQy 1280 gS rFkk e-l- 8 gS rks rksmu mudk y-l- Kkr djsaA la[;kvksa dk y-l- D;k gksxk\ (a) 200 (b) 250 (a) 160 (b) 150 (c) 100 (d) 150 (c) 120 (d) 140 66. The HCF of two numbers, each having three digits, 59. The least multiple of 7, which leaves the remainder is 17 and their LCM is 714. The sum of the numbers 4, when divided by any of 6, 9 15 and 18, is: will be: 7 dk U;wure xq.kkad D;k gS] ftlesa 6] 9] 15 rFkk 18 rhu vadks dh nks la[;kvksa dk e-l- 17 gS vkSj y-l- ls Hkkx nsus ij 4 'ks"k cprk gS\ 714 gS] rks la[;kvksa dk ;ksx D;k gksxk\ (a) 76 (b) 94 (a) 289 (b) 391 (c) 184 (d) 364 (c) 221 (d) 731 60. The largest number of five digits which, when 67. The HCF and product of two numbers are 15 and divided by 16, 24, 30, or 36 leaves the same 6300 respectively. The number of possible pairs of remainder 10 in each case, is: the numbers is: ik¡p vadksa dh vfèkdre la[;k D;k gS] ftlesa 16] 24] nks la[;kvksa dk e-l- o xq.kuiQy Øe'k% 15 rFkk 6300 30 ;k 36 ls Hkkx nsus ij izR;sd fLFkfr esa 10 'ks"k cprk gS] bl rjg ds la[;kvksa ds fdrus laHkkfor tksM+s gks gSA ldrs gS\ (a) 99279 (b) 99370 (a) 4 (b) 3 (c) 99269 (d) 99350 61. The least number, which is a perfect square and is (c) 2 (d) 1 68. The smallest number, which when divided by 5, 10, divisible by each of the numbers 16, 20 and 24 is: 12 and 15, leaves remainder 2 in each case, but when og U;wure oxZ la[;k D;k gS] tks 16] 20 rFkk 24 izR;sd divided by 7 leaves no remainder, is: ls foHkkftr gS\ (a) 1600 (b) 3600 og U;wure la[;k D;k gS] ftlesa 5] 10] 12 rFkk 15 ls (c) 6400 (d) 14400 Hkkx nsus ij izR;sd fLFkfr esa 2 'ks"k cprk gS ysfdu 7 ls 62. The number nearest to 43582 divisible by each of Hkkx nsus ij dksbZ 'ks"k ugha cprk gS\ 25, 50 and 75 is: (a) 189 (b) 182 43582 ds fudVre og la[;k D;k gS] tks 25] 50 rFkk (c) 175 (d) 91 75 izR;sd ls foHkkftr gSA 69. What least number must be subtracted from 1936 (a) 43500 (b) 43650 so that the resulting number when divided by 9, 10 (c) 43600 (d) 43550 and 15 will leave in each case the same remainder 7? 63. Three sets of 336 English books, 240 Mathematics books and 96 Science books have to be stacked in 1936 esa ls og dkSu&lh U;wure la[;k ?kVk;h tk, fd such a way that all the books are stored subject- izkIr la[;k esa 9] 10 rFkk 15 ls Hkkx nsus ij izR;sd wise and the height of each stack is the same. Total fLFkfr esa 7 'ks"k cps\ number of stacks will be: (a) 37 (b) 36 vaxzsth] xf.kr rFkk foKku dh fdrkcksa ds rhu lsV esa (c) 39 (d) 30 Øe'k% 336] 240 rFkk 96 fdrkcsa gSa bu fdrkcksa dks bl rjg ls LVsdks esa yxkuk gSA fd izR;sd LVsd70.dh Å¡pkbZ The least number, which when divided by 18, 27 and 36 separately leaves remainders 5, 14, 23 cjkcj gS vkSj lHkh fdrkcsa fo"k;okj qaMks esa bl rjg ck¡Vrk gS fd izR;sd >qaM esa cjkcj 108. Find the greatest number which will exactly divide i'kq gks vkSj xk; rFkk HksaM+ vyx&vyx gks] ;fn ;s >qaM 200 and 320. ftruk cM+k gks ldrk gS mruk cM+k gks] rks ,d >qaM esa og vfèkdre la[;k Kkr djsa tks 200 rFkk 320 dks fdrus i'kq gSa rFkk >qaMksa dh la[;k fdruh gS\ iw.kZr% foHkkftr dj ns\ (a) 15 and 228 (b) 9 and 380 (a) 10 (b) 20 (c) 45 and 76 (d) 46 and 75 (c) 16 (d) 40 102. The greatest 4-digit number exactly divisible by 10, 15, 20 is 109. 84 Maths books, 90 Physics books and 120 Chemistry books have to be stacked topic wise. How 4 vadks dh vfèkdre la[;k tks 10] 15 rFkk 20 ls many books will be their in each stack so that each iw.kZr% foHkkftr gks] D;k gS\ stack will have the same height too? (a) 9990 (b) 9960 84 xf.kr] 90 HkkSfrdh rFkk 120 jlk;u ds fdrkcksa dks (c) 9980 (d) 9995 fo"k;koj rjhds ls LVsdksa esa yxkuk gS] izR;sd LVsd esa 103. The greatest number that divides 411, 684, 821 and fdruh fdrkcs gksaxh fd izR;sd LVsdksa dh Å¡pkbZ cjkcj leaves 3, 4 and 5 as remainders, respectively, is: gks\ og vfèkdre la[;k D;k gS ftlls 411] 684] 821 esa (a) 12 (b) 18 Hkkx nsus ij Øe'k 3] 4 rFkk 5 'ks"k cprk gS\ (c) 6 (d) 21 (a) 245 (b) 146 110. The greatest number that will divide 729 and 901 (c) 136 (d) 204 leaving remainders 9 and 5 respectively is: 104. The ratio of two numbers is 3 : 4 and their HCF is 5. Their LCM is: og vfèkdre la[;k D;k gS] ftlls 729 rFkk 901 esa Hkkx nsus ij Øe'k% 9 rFkk 5 'ks"k cps\ nks la[;kvksa dk vuqikr 3 % 4 gS rFkk mudk e-l- 5 gS] rks y-l- Kkr djsa\ (a) 15 (b) 16 (c) 19 (d) 20 (a) 10 (b) 60 111. Three numbers are in the ratio 1 : 2 : 3 and their (c) 15 (d) 12 HCF is 12. The numbers are 105. If A and B are the HCF and LCM respectively of two algebraic expressions x and y , and A+b = x + y, rhu la[;k,¡ 1 % 2 % 3 ds vuqikr esa gS] mudk e-l- 12 then the value of A3+B3 is gS] rks la[;k,¡ Kkr djsa\ nks chtxf.krh; O;atdks x rFkky dk e-l- o y- l- (a) 12, 24, 36 (b) 5, 10, 15 Øe'k%A rFkkB gS] ;fnA+B = x + y, gks] rks A3 + B3 (c) 4, 8, 12 (d) 10, 20, 30 dk eku Kkr djsa\ 112. If x : y be the ratio of two whole numbers and z be (a) x3 – y3 (b) x3 their HCF, then the LCM of those two number is : (c) y3 (d) x3 + y3 ;fn nks iw.kZ la[;kvksa dkx vuqikr : y gS rFkk mudk e- 106. The HCF and LCM of two numbers are 44 and 264 l- z gS] rks mudk y-l- D;k gksxk\ respectively. If the first number is divided by 2, the quotient is 44. The other number is: xz (a) yz (b) y nks la[;kvksa ds e-l- vkSj y-l- Øe'k% 44 rFkk 264 gS] ;fn igyh la[;k esa 2 ls Hkkx fn;k tkrk gS] rks HkkxiQy xy 44 gS] rks nwljh la[;k Kkr djsa\ (c) z (d) xyz Contact No. : 9555202436, 9716761136 9 oDr cnyrk gS] fQj cnysxk A lkjk tgk¡ viuk gksxk AA A-7, Top Floor, Jai Building, Commercial Complex Near Chawla Restaurant, Dr Mukherjee Nagar, Delhi-110009  ABHINAY MATHS CLASSES 113. If the HCF and LCM of two consecutive (positive) nks èkukRed iw.kkZdksa dk y-l- cM+h la[;k dk nks xquk even numbers be 2 and 84 respectively, then the sum gSA NksVh la[;k rFkk e-l- dk varj 4 gS] rks NksVh la[;k of the numbers is: Kkr djsaA nks yxkrkj èkukRed le la[;kvksa dk e-l- rFkk y-l- (a) 12 (b) 6 Øe'k% 2 rFkk 84 gS] rks la[;kvksa dk ;ksx Kkr djsa\ (c) 8 (d) 10 (a) 30 (b) 26 120. The HCF (GCD) of a, b is 12, a, b are positive (c) 14 (d) 34 integers and a > b > 12. The smallest value of (a, b) 3 10 5 114. If P = 2.3.5 : Q = 2.3.7, then HCF of P and Q is: are respectively ;fn P = 23.310.5 : Q = 25.3.7, gS] rks P rFkkQ dk e- a, b, dk e-l- 12 gS rFkk a vkSjb èkukRed iw.kk±d gSA l- Kkr djsaA a > b > 12 gS] rks (a, b) dk U;wure eku D;k gksxk\ (a) 2.3.5.7 (b) 3.23 (a) 12, 24 (b) 24, 12 (c) 22.37 (d) 25.310.5.7 115. A fraction becomes 1/6 when 4 is subtracted from (c) 24, 36 (d) 36, 24 its numerator and 1 is added to its denominator. If 2 121. Product of two co-prime numbers is 117. Then their and 1 are respectively added to its numerator and LCM is: the denominator, it becomes 1/3. Then, the LCM of nks lgvHkkT; la[;kvksa dk xq.kuiQy 117 gS] rks mudk the numerator and denominator of the said fraction, must be y-l- Kkr djsaA (a) ij117 ,d fHkUu ds va'k esa ls 4 ?kVkus ij gj esa 1 tksM+us (b) 9 fHkUu 1@6 gks tkrh gSA ;fn muds va'k rFkk gj esa(c) Øe'k%13 (d) 39 2 vkSj 1 tksM+s tkrs gSa rks ;g 1@3 gks tkrh gSA fHkUu ds 122. The product of two numbers is 2160 and their HCF is 12. Number of such possible pairs are: va'k rFkk gj dk y-l- Kkr djsaA (a) 14 (b) 350 nks la[;kvksa dk xq.kuiQy 2160 gS vkSj mudk e-l- 12 (c) 5 (d) 70 gS] rks bl rjg dh la[;k ds fdrus laHkkfor tksM+s gksxsa\ 116. HCF of 2/3, 4/5 and 6/7 is: (a) 1 (b) 2 2@3] 4@5 vkSj 6@7 dk e-l- D;k gksxk\ (c) 3 (d) 4 123. LCM of two numbers is 2079 and their HCF is 27. 48 2 (a) (b) If one of the number is 189, the other number is : 105 105 nks la[;kvksa dk y-l- 2079 gS rFkk mudk e-l- 27 gSA (c) 1 (d) 24 ;fn ,d la[;k 189 gS] rks nwljh la[;k Kkr djsaA 105 105 (a) 297 (b) 584 117. What is the greatest number which will divide 110 (c) 189 (d) 216 and 128 leaving a remainder 2 in each case? 124. Five bells begin to toll together and toll respectively og vfèkdre la[;k D;k ftlls 110 rFkk 128 dks Hkkx at intervals of 6, 7, 8, 9 and 12 seconds. After how nsus ij izR;sd fLFkfr esa 2 'ks"k cprk gS\ many seconds will they toll together again? (a) 8 (b) 18 ik¡p ?kafV;k¡ ,d lkFk ctrh gS vkSj os Øe'k% 6] 7] 8] (c) 28 (d) 38 9 rFkk 12 lsds.Mksa ds varjky ij ctrh gS] rks fdrus 118. A milk vendor has 21 lt of cow milk, 42 lt of toned milk and 63 lt of double toned milk. If he wants so lsds.M ds ckn os iqu% lkFk ctsxh\ pack them in cans so that each can contains same lt (a) 72 sec. (b) 612 sec. of milk and does not want to mix any two kinds of (c) 504 sec. (d) 318 sec. milk in a can, then the least number of cans required is: 2 4 5 125. LCM of , , is: ,d nwèk foØsrk ds ikl 21 yh- xk; dk nwèk] 42 VksUM nwèk 3 9 6 rFkk 63 yh- Mcy VksUM nwèk gSA ;fn og bu nwèkksa 2 4dks dsuksa 5 esa bl izdkj iSd djuk pkgrk gS fd izR;sd dsu esa cjkcj 3 , 9 rFkk6 dk y-l- D;k gksxk\ ek=kk esa nwèk gks vkSj nks izdkj ds nwèkksa dks ,d dsu esa og feykrk Hkh ugha gS] rks dsuksa dh U;wure la[;k Kkr (a) djsaA 8 (b) 20 (a) 3 (b) 6 27 3 (c) 9 (d) 12 10 20 119. The LCM of two positive integers is twice the larger (c) (d) 3 27 number. The difference of the smaller number and the GCD of the two numbers is 4. The smaller 126. The least number which when divided by 6, 9, 12, number is: 15, 18 leaves the same remainder 2 in each case is : Contact No. : 9555202436, 9716761136 10 oDr cnyrk gS] fQj cnysxk A lkjk tgk¡ viuk gksxk AA A-7, Top Floor, Jai Building, Commercial Complex Near Chawla Restaurant, Dr Mukherjee Nagar, Delhi-110009  ABHINAY MATHS CLASSES og U;wure la[;k D;k gS ftlesa 6] 9] 12] 15 rFkk 18 nks la[;kvksa dk y?kqÙke lekiorZd muds egÙke lekiorZd ls Hkkx nsus ij izR;sd fLFkfr esa 2 'ks"k cprk gks\dk 12 xquk gSA egÙke lekiorZd vkSj y?kqÙke lekiorZd (a) 180 (b) 176 dk ;ksx 403 gSA ;fn muesa ls ,d la[;k 93 gS] rks nwljh (c) 182 (d) 178 la[;k D;k gS\ 127. The HCF of x6 – 1 and x4 + 2x3 – 2x1 – 1 is: (a) 116 (b) 124 x – 1 vkSjx + 2x – 2x – 1 dk e-l- D;k gksxkA 6 4 3 1 (c) 112 (d) 120 (a) x2 + 1 (b) x – 1 134. The number of pair of positive integers whose sum 2 (c) x –1 (d) x + 1 is 99 and HCF is 9 is: 128. The greatest number by which 2300 and 3500 are èkukRed iw.kkZdksa ds ,sls ;qXeksa dh la[;k ftudk ;ksx 99 divide leaving the remainders of 32 and 56 gS vkSj egÙke lekiorZd 9 gSµ respectively. (a) 5 (b) 2 og vfèkdre la[;k D;k gS ftlls 2300 rFkk 3500 esa (c) 3 (d) 4 Hkkx nsus ij Øe'k% 32 rFkk 56 'ks"k cprk gks\135. The ratio of two numbers is 3 : 4 and their LCM is (a) 168 (b) 42 120. The sum of numbers is: (c) 48 (d) 136 nks la[;kvksa dk vuqikr 3 % 4 gS vkSj mudk y?kqÙke 129. Let, x be the smallest number, which when added to lekoR;Z 120 gSA mu la[;kvksa dk ;ksx gSµ 2000 makes the resulting number divisible by 12, (a) 70 (b) 35 16, 18 and 21. The sum of the digits of x is: (c) 140 (d) 105 eku ysa fdx ,d y?kqÙke la[;k gS ftls tc 2000 esa 136. The greatest four digit number which is exactly tksM+k tk,] rks ifj.kkeh la[;k 12] 16] 18 vkSj 21 lsdivisible by each one of the numbers 12, 18, 21 and foHkkT; gks tkrhx ds gSA vadksa dk ;ksx gSA 28. (a) 6 (b) 5 pkj vadksa dh lcls cM+h la[;k tks 12] 18] 21 o 28 (c) 7 (d) 8 izR;sd la[;kvks ls iw.kZr;k foHkkT; gksA 130. Let x be the least number, which when divided by (a) 9828 (b) 9882 5, 6, 7 and 8 leaves a remainder 3 in each case but (c) 9928 (d) 9288 when divided by 9 leaves remainder 0. The sum of 137. The smallest five digit number which is divisible digits of x is: by 12, 18 and 21 is: eku ysx U;wure la[;k] ftls 5] 6] 7 vkSj 8 ls ik¡p vadksa okyh og y?kqÙke la[;k crkb, tks 12] 18 foHkkftr djus ij izR;sd fLFkfr esa 3 'ks"kiQy jgrkvkSj gS 21 ls foHkkT; gksA ijarq 9 ls foHkkftr fd, tkus ij dksbZ 'ks"kiQy ugha (a) 10080 (b) 30256 jgrkAx ds vadksa dk ;ksx D;k gS\ (c) 10224 (d) 50321 (a) 24 (b) 21 138. A number between 1000 and 2000 which when (c) 22 (d) 18 divided by 30, 36 and 80 gives a remainder 11 in 131. A number when divided by 361 gives remainder each case is: 47. When the same number is divided by 19 then 1000 vkSj 2000 ds chp dksbZ ,slh la[;k gS ftls ;fn find the remainder? 30] 36 vkSj 80 ls foHkDr fd;k tk, rks izR;sd fLFkfr ,d la[;k dks tc 361 ls foHkkftr fd;k tk,] rks esa 'ks"k 11 gksxkA 'ks"kiQy 47 jgrk gSA ;fn mlh la[;k dks 19 ls foHkkftr (a) 11523 (b) 1451 fd;k tk,] rks 'ks"kiQy fdruk jgsxk\ (c) 1641 (d) 1712 (a) 9 (b) 1 139. The difference between the greatest and least prime (c) 8 (d) 3 numbers which are less than 100 is: 132. The H.C.F and L.C.M of two numbers are 21 and egÙke vkSj y?kqÙke vHkkT; la[;kvksa tks 100 ls de gksa] 84 respectively. If the ratio of the two numbers is 1 : 4, then the larger of the two numbers is: ds chp dk vUrj D;k gksxk\ (a) 95 (b) 96 2 la[;kvksa dk egÙke lekiorZd vkSj y?kqre lekioR;Z (c) 97 (d) 94 Øe'k% 21 vkSj 84 gSaA ;fn nks la[;kvksa dk vuqikr 1% 140. The number between 4000 and 5000 that is divisible 4 gS] rks nks la[;kvksa esa ls cM+h la[;k gksxhA by each of 12, 18, 21 and 32 is: (a) 48 (b) 12 4000 vkSj 5000 ds chp ,slh la[;k tks 12] 18] 21 (c) 84 (d) 108 rFkk 32 ls foHkkT; gks] fuEufyf[kr esa ls D;k gksxh\ 133. The LCM of two numbers is 12 times their HCF. (a) 4203 (b) 4023 The sum of the HCF and LCM is 403. If one of the number is 93, then the other is: (c) 4032 (d) 4302 Contact No. : 9555202436, 9716761136 11 oDr cnyrk gS] fQj cnysxk A lkjk tgk¡ viuk gksxk AA A-7, Top Floor, Jai Building, Commercial Complex Near Chawla Restaurant, Dr Mukherjee Nagar, Delhi-110009  ABHINAY MATHS CLASSES ANSWER KEY 1. (c) 2. (c) 3. (c) 4. (b) 5. (c) 6. (d) 7. (a) 8. (a) 9. (d) 10. (a) 11. (b) 12. (d) 13. (a) 14. (c) 15. (b) 16. (a) 17. (c) 18. (c) 19. (b) 20. (d) 21. (a) 22. (c) 23. (c) 24. (a) 25. (a) 26. (b) 27. (b) 28. (c) 29. (a) 30. (b) 31. (b) 32. (d) 33. (c) 34. (d) 35. (c) 36. (c) 37. (c) 38. (c) 39. (b) 40. (d) 41. (b) 42. (b) 43. (b) 44. (a) 45. (c) 46. (d) 47. (d) 48. (b) 49. (c) 50. (d) 51. (b) 52. (a) 53. (d) 54. (d) 55. (b) 56. (d) 57. (a) 58. (a) 59. (d) 60. (b) 61. (b) 62. (b) 63. (a) 64. (a) 65. (c) 66. (c) 67. (c) 68. (b) 69. (c) 70. (a) 71. (c) 72. (c) 73. (d) 74. (a) 75. (a) 76. (d) 77. (c) 78. (c) 79. (a) 80. (d) 81. (b) 82. (d) 83. (a) 84. (b) 85. (d) 86. (c) 87. (b) 88. (c) 89. (a) 90. (c) 91. (a) 92. (d) 93. (b) 94. (b) 95. (d) 96. (d) 97. (b) 98. (b) 99. (a) 100. (b) 101. (c) 102. (b) 103. (c) 104. (b) 105. (d) 106. (c) 107. (c) 108. (d) 109. (c) 110. (b) 111. (a) 112. (d) 113. (b) 114. (b) 115. (a) 116. (b) 117. (b) 118. (b) 119. (c) 120. (d) 121. (a) 122. (b) 123. (a) 124. (c) 125. (b) 126. (c) 127. (c) 128. (b) 129. (c) 130. (d) 131. (a) 132. (c) 133. (b) 134. (a) 135. (a) 136. (a) 137. (a) 138. (b) 139. (a) 140. (c) Contact No. : 9555202436, 9716761136 12 oDr cnyrk gS] fQj cnysxk A lkjk tgk¡ viuk gksxk AA A-7, Top Floor, Jai Building, Commercial Complex Near Chawla Restaurant, Dr Mukherjee Nagar, Delhi-110009