Question

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

• A. 24
• B. 48
• C. 72
• D. 96

Hint:

Use HCF $\times$ LCM = product of numbers to find the second number.

Answer 1

The Correct Option is B

- Step 1: For two numbers $a$ and $b$, HCF $\times$ LCM = $a \times b$.
- Step 2: Given HCF = 12, LCM = 144, $a = 36$.
- Step 3: So, $12 \times 144 = 36 \times b \implies b = \frac{12 \times 144}{36} = 48$.
- Step 4: Verify: HCF of 36 and 48 is 12, LCM is $36 \times 48 \div 12 = 144$, matches.
- Step 5: Option (2) is 48, correct.