Find the LCM and HCF of the following integers by applying the prime factorization method :

96 and 404

Given numbers are 96 and 404.

The prime factorization of 96 and 404 gives:

Here, 2² is the smallest power of the common factor 2.

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

2⁵ × 3¹ × 101¹ are the greatest powers of the prime factors 2, 3 and 101 respectively involved in the given numbers.

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