Question

Find the LCM and HCF of the following pair of integers and verify that LCM × HCF = Product of the integers.

96 and 120

Answer 1

Given: 96 and 120.

Step-wise calculation:

1. Prime factorisation:

96 = 2⁵ × 3

120 = 2³ × 3 × 5

2. HCF (product of common primes with smallest powers):

Common primes: 2 (min power 3) and 3 (min power 1)

HCF = 2³ × 3

= 8 × 3

= 24

3. LCM (product of primes with largest powers):

Take 2⁵, 3¹, 5¹

LCM = 2⁵ × 3 × 5

= 32 × 3 × 5

= 480

4. Verify LCM × HCF = Product of the integers:

96 × 120 = 11,520

HCF × LCM = 24 × 480 = 11,520

Equality holds.

HCF = 24, LCM = 480 and LCM × HCF = 96 × 120 = 11,520 (verified).