Question

The HCF of two numbers is 12, and their LCM is 144. If one number is 48, find the other.

• A. 36
• B. 48
• C. 60
• D. 72

Hint:

Use $\text{HCF} \times \text{LCM} = a \times b$ and verify with HCF and LCM calculations.

Answer 1

The Correct Option is A

- Step 1: Use HCF-LCM property. $\text{HCF} \times \text{LCM} = a \times b$. Given: HCF = 12, LCM = 144, $a = 48$.
- Step 2: Solve. $12 \times 144 = 48 \times b \implies 1728 = 48b \implies b = \frac{1728}{48} = 36$.
- Step 3: Verify. HCF(48, 36) = 12. LCM = $\frac{48 \cdot 36}{12} = 144$. Matches.
- Step 4: Check options. $b = 36$ is option (1).
- Step 5: Conclusion. Option (1) 36 is correct.