Question

Find the LCM and HCF of the pair of integers 852 and 1491 and verify that LCM x HCF = Product of two numbers.

Answer 1

Given numbers are 852 and 1491

The prime factorization of 852 and 1491 gives:

852 = 2 × 2 × 3 × 71 and 1491 = 3 × 7 × 71

Therefore, the H.C.F of these two integers = 3 × 71 = 213

Now, the L.C.M of 96 and 404 = 2 × 2 × 3 × 7 × 71 = 5964

Now, we have to verify

L.H.S = L.C.M × H.C.F = 5964 × 213 = 1270332

R.H.S = Product of two numbers = 852 × 1491 = 1270332

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

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