The HCF of two numbers is 6 and their LCM is 432. If one of the numbers is 48,…

Concept

For two positive integers a and b, the product of the numbers equals the product of their HCF and LCM: a × b = HCF(a, b) × LCM(a, b). Therefore, when one number and both measures are known, the other number is obtained by dividing HCF × LCM by the known number.

Application

1. Let the other number be x.

2. Apply the identity: 48 × x = 6 × 432.

3. Calculate the product on the right: 6 × 432 = 2592, so 48 × x = 2592.

4. Divide both sides by 48: x = 2592 ÷ 48 = 54.

Cross-check

The pair 48 and 54 has HCF 6. Also, (48 × 54) ÷ 6 = 432, so its LCM is 432; both given conditions are satisfied.

Thus, the other number is 54.