The HCF and LCM of two numbers are 3 and 1170 respectively. If one of the numbers is 45, find the other.
Understand the Problem
The question is asking to find the other number when given the HCF (3), LCM (1170), and one of the numbers (45). To solve it, we can use the relationship between HCF, LCM, and the two numbers involved.
Answer
The other number is $78$.
Answer for screen readers
The other number is $78$.
Steps to Solve
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Use the relationship of HCF and LCM We know the relationship between the two numbers (let's call them $a$ and $b$), HCF (which is 3), and LCM (which is 1170) is given by the formula: $$ HCF \times LCM = a \times b $$
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Insert known values into the equation We can substitute the known values into the equation. One of the numbers is given as 45, so we have: $$ 3 \times 1170 = 45 \times b $$
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Calculate the left side of the equation Calculate the left side: $$ 3 \times 1170 = 3510 $$ So the equation becomes: $$ 3510 = 45 \times b $$
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Solve for the unknown number $b$ To find $b$, divide both sides by 45: $$ b = \frac{3510}{45} $$
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Perform the division Now, perform the division: $$ b = 78 $$
The other number is $78$.
More Information
This problem demonstrates the use of HCF and LCM to find a missing number using a fundamental relationship. It's a useful technique in number theory and can be applied in various mathematical settings.
Tips
- Forgetting to use the correct formula. Ensure to remember that the product of HCF and LCM is equal to the product of the two numbers.
- Incorrect calculations while performing division or multiplication. Always double-check arithmetic to avoid mistakes.
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