Question

Find the LCM and HCF of the pair of integers 36 and 64 and verify that LCM x HCF = Product of two numbers.

Answer 1

Given numbers are 36 and 64

The prime factorization of 36 and 64 gives:

36 = 2 × 2 × 3 × 3 and 64 = 2⁶

Therefore, the H.C.F of these two integers = 2 × 2 = 4

Now, the L.C.M of 36 and 64 = 3 × 3 × 2⁶ = 576

Now, we have to verify

L.H.S = L.C.M × H.C.F = 576 × 4 = 2304

R.H.S = Product of two numbers = 36 × 64 = 2304

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

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