If HCF (a, 8) = 4 and LCM (a, 8) = 24, then ‘a’ is

Concept

For any two positive integers, the product of the numbers equals the product of their HCF and LCM.

In symbols, x × y = HCF(x, y) × LCM(x, y). This identity determines an unknown number when the other three quantities are known.

Application

1. Let the unknown number be a. Pairing it with 8 gives a × 8 = 4 × 24 by the HCF–LCM identity.

2. Multiply the known factors: 4 × 24 = 96, so 8a = 96.

3. Divide both sides by 8: a = 96 ÷ 8 = 12.

Cross-check

HCF(12, 8) = 4 and LCM(12, 8) = 24, so both given conditions hold. Therefore, a = 12.