Two natural numbers have HCF 12 and LCM 72. If one number is 24, what is the difference between the two numbers?

Introduction:
The product of two numbers equals the product of their HCF and LCM. Knowing one number allows us to find the other directly, then compute the difference.

Given Data / Assumptions:

• HCF = 12
• LCM = 72
• One number = 24

Concept / Approach:
a * b = HCF * LCM. Solve for the unknown and subtract to find the difference.

Step-by-Step Solution:

Verification / Alternative check:
HCF(24, 36) = 12 and LCM(24, 36) = 72, confirming consistency.

Why Other Options Are Wrong:
18, 21, and 24 do not match the computed difference for the consistent pair.

Common Pitfalls:
Using sum instead of product relation, or forgetting to check that the derived pair satisfies both HCF and LCM values.

Final Answer:
12