Question

Find the LCM and HCF of the pair of integers 96 and 404 and verify that LCM X HCF = Product of two numbers.

Answer 1

Given numbers are 96 and 404

The prime factorization of 96 and 404 gives:

96 = 2⁵ × 3 and 404 = 2² × 101

Therefore, the H.C.F of these two integers = 2² = 4

Now, the L.C.M of 96 and 404 = 2 × 2 × 2 × 2 × 2 × 3 × 101 = 9696

Now, we have to verify

L.H.S = L.C.M × H.C.F = 9696 × 4 = 38784

R.H.S = Product of two numbers = 96 × 404 = 38784

Hence, L.H.S = R.H.S

So, the product of two numbers is equal to the product of their HCF and LCM.