Find the LCM and HCF of the following integers by applying the Prime factorisation method

1) 12,15 & 21

2) * 17,23 & 29

3) 8,9 & 25

Sol. 1) Prime factors of 12 = 2 x 2 x 3

Prime factors of 15 = 3 x 5

Prime factors of 21 = 3 x 7

So, HCF (Product of all common factors of given three numbers 12, 15 and 21) = 3

and LCM of 12, 15 and 21 = Product of common factors with other remaining factors i. e., LCM = 3 x 22 x 5 x 7 = 420

2) Prime factors of 17 = 17 x 1

Prime factors of 23 = 23 x 1

Prime factors of 29 = 29 x 1

So, HCF of 17, 23 and 29 = 1

and their LCM = 17 x 23 x 29 = 11339

3) Prime factors of 8 = 2 x 2 x 2

Prime factors of 9 = 3 x 3

Prime factors of 25 = 5 x 5

So, HCF of 8, 9 and 25 is 1 because their is no common factors in the prime factorization of 8, 9 and 25.

Now LCM of 8,9 and 25 = 8 x 9 x 25=1800