Question

Find the LCM and HCF of the following integers by the prime factorization method.
12, 15 and 21 ​

Answer 1

Answer:

hcf =3 and lcm = 420

Step-by-step explanation:

(i) 12, 15 and 21 12 = 2 × 2 × 3 = 22 × 3 15 = 3 × 5 and 21 = 3 × 7 For HCF, we find minimum power of prime factor H.C.F. = (3)1 = 3 For LCM, taking maximum power of prime factors L.C.M. = 22 × 3 × 5 × 7 = 4 × 3 × 5 × 7 = 420 So H.C.F. = 3 L.C.M. = 420

Answer 2

EXPLANATION

For H.C.F and L.C.M first we need to find the

prime factorisation of the given numbers.

So,

12 = 2 × 2 × 3 = 2 = 2^ 2 × 3

15 = 3 × 5

21 = 3 × 7

H.C.F

For H.C.F, first we need to take the product of the smallest power of each common prime factors in the numbers . So ,

H.C.F(12, 15 , 21) = 3

L.C.M

For L.C.M , we need to take the product of the greatest power of each prime factor involved in the numbers. Then ,

L.C.M.(12, 15 , 21) = 2^2 × 3 × 5 × 7 = 420

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