Question

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

72 and 120

Answer 1

Given: 72 and 120

Step-wise calculation:

1. Prime factorisation

72 = 8 × 9 

= 2³ × 3² 

120 = 8 × 15

= 2³ × 3¹ × 5¹

2. HCF (product of common primes with lowest powers)

HCF = 2³ × 3¹

= 8 × 3

= 24

3. LCM (product of all primes with highest powers)

LCM = 2³ × 3² × 5¹

= 8 × 9 × 5

= 360

Recall: For two numbers, HCF × LCM = Product of the two numbers.

Verification HCF × LCM = 24 × 360 = 8640

Product of the integers = 72 × 120 = 8640

So HCF × LCM = Product of the integers (verified).

HCF = 24, LCM = 360 and 24 × 360 = 72 × 120 = 8640 (verification complete).