Question

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

404 and 96

Answer 1

Given: 404 and 96

Step-wise calculation:

1. Prime factorisation:

404 = 4 × 101

= 2² × 101

96 = 32 × 3

= 2⁵ × 3

2. HCF (common primes with smallest exponents):

HCF = 2^min(2, 5)

= 2²

= 4

3. LCM (all primes with largest exponents):

LCM = 2⁵ × 3 × 101

= 32 × 303

= 9696

4. Verification:

Product of the integers = 404 × 96

= 38,784

HCF × LCM = 4 × 9,696

= 38,784

Hence, HCF × LCM = Product of the integers.

HCF = 4, LCM = 9,696 and LCM × HCF = 38,784 = 404 × 96 (verified).