Find the HCF of 96 and 404 by Prime Factorisation and Use it to Find the LCM

Answer: Let us assume that, 

X= 404

Y = 96

Now ,express the term X and Y as a product of prime number:

X=404 = 2 × 2 × 101

Y=96 = 2 × 2 × 2 × 2 × 2 × 3

 LCM of X and Y is 2 × 2 × 2 × 2 × 2 × 101 × 3 = 9696

HCF of X and Y is 2 × 2 = 4

Now , HCF × LCM  = 4 × 9696 = 38784

Product of two given numbers X × Y = 38784

Hence, HCF × LCM is equal to the product of two given numbers.

∴ The HCF of X and Y is 4, and the LCM of X and Y is 9696.