Question:
Find HCF and LCM of 404 and 96 and verify that HCF × LCM = product of two given numbers.
Solution:
Prime factorisation:
404 = 2 × 2 × 101
96 = 2 × 2 × 2 × 2 × 2 × 3
HCF (404, 96) = 2 × 2
= 4
LCM (404, 96) = 2 × 2 × 2 × 2 × 2 × 3 × 101
= 9696
Now, LCM × HCF = 9696 × 4
= 38784
Product of 404 and 96 = 404 × 96
= 38784
Hence, HCF × LCM = product of two given numbers.