Question

Find LCM and HCF of the integers 8, 9, and 25 by using prime factorization method.

Answer 1

Given numbers are 8, 9 and 25

Factorization of 8, 9 and 25

8 = 2 × 2 × 2 × 1 = 2³ × 1

9 = 3 × 3 × 1 = 3² × 1

25 = 5 × 5 × 1 = 5² × 1

Here, 1¹ is the smallest power of the common factor 1.

So, HCF (8, 9, 25) = 1

2³ × 3² × 5² are the greatest powers of the prime factors 2, 3 and 5 respectively involved in the given three numbers .

LCM of these three integers = 2 × 2 × 2 × 3 × 3 × 5 × 5 = 1800