Question

Find the LCM and HCF of the integers 6 and 21 by applying the prime factorization method.

Answer 1

Given numbers are 6 and 21.

The prime factorization of 6 and 21 gives:

Here, 3¹ is the smallest power of the common factor 3.

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

2¹ × 3¹ × 7¹ are the greatest powers of the prime factors 2, 3 and 7 respectively involved in the given numbers.

Now, L.C.M of 6 and 21 is 2 ×3 × 7 = 42