Question

The HCF of two numbers is 12, and their LCM is 144. If one number is 36, what is the other number?

• A. 48
• B. 60
• C. 72
• D. 96

Hint:

Use the formula $a \times b = \text{HCF} \times \text{LCM}$ to find the second number when HCF, LCM, and one number are given.

Answer 1

The Correct Option is A

- Step 1: Let the two numbers be $a$ and $b$, with $a = 36$. Given HCF = 12 and LCM = 144.
- Step 2: Use the relation: $a \times b = \text{HCF} \times \text{LCM}$.
- Step 3: Substitute: $36 \times b = 12 \times 144$.
- Step 4: Calculate: $36b = 1728$, so $b = \dfrac{1728}{36} = 48$.
- Step 5: Verify: HCF of 36 and 48 is 12 (factors check); LCM is $36 \times 48 \div 12 = 144$.
- Step 6: Check options: Option (a) is 48, which matches.