Question

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

• A. 24
• B. 48
• C. 60
• D. 72

Hint:

For any two numbers, HCF × LCM = product. This can quickly find a missing number if HCF, LCM, and one number are known.

Answer 1

The Correct Option is B

- Step 1: Relation between HCF, LCM, and product - For two positive integers $a$ and $b$: \[ \text{HCF}(a,b) \times \text{LCM}(a,b) = a \times b \] 
- Step 2: Substitute known values - \[ 12 \times 144 = 36 \times b \] 
- Step 3: Solve for $b$ - \[ b = \frac{12 \times 144}{36} = \frac{1728}{36} = 48 \] 
- Step 4: Verification - HCF(36, 48) = 12, LCM(36, 48) = $\frac{36 \times 48}{12} = 144$. Both match the given. 
- Step 5: Conclusion - The other number is $48$, matching option (2).