Mathematics HCF and LCM Quiz

Relationship between HCF, LCM, and Numbers

• The product of two numbers is equal to the product of their HCF and LCM.
• The HCF is the highest common factor of two numbers, representing the largest number that divides both of them evenly.
• The LCM is the least common multiple of two numbers, representing the smallest number that is a multiple of both.

Finding the Other Number

• Calculation: To find the other number, use the formula:

  • (Number 1 * Number 2) = HCF * LCM
  • Rearranged to solve for Number 2: Number 2 = (HCF * LCM) / Number 1

• Applying to the example:

  • Number 1 = 45
  • HCF = 3
  • LCM = (45 * Number 2) / 3
  • To find Number 2, we need the LCM.

Determining Factors of the LCM

• If the LCM of two numbers is 1170, it indicates that 1170 is divisible by both numbers.
• Any number that is a factor of the LCM (1170) shares a common factor with both numbers.
• Since the HCF is 3, both numbers have 3 as a factor.

Implication of Sharing the Same HCF

• If two numbers share the same HCF of 3, it means that both numbers are divisible by 3.
• It does not necessarily imply they have other common factors, but it guarantees that they have 3 in common.