Question

2. Find the LCM and HCF of the following integers by the prime factorization method.
(i) 12, 15 and 21
(ii) 17, 23, and 29
(iii) 8, 9 and 25
(iv) 72 and 108
(v) 306 and 657​

Answer 1

Answer:

1)

Facors of 12 = 2 x 2 x 3

Factors of 15 = 3 x 5

Factors of 21 = 3 x 7

LCM = 2 x 2 x 3 x 5 x 7 = 420

HCF = 3

2)

Facors of 17 = 17

Factors of 23 = 23

Factors of 29 = 29

LCM = 17 x 23 x 29 = 11339

HCF = Nothing

3)

Facors of 8 = 2 x 2 x 2

Factors of 9 = 3 x 3

Factors of 25 = 5 x 5

LCM = 2 x 2 x 2 x 3 x 3 x 5 x 5

HCF = Nothing

4)

Facors of 72 = 2 x 2 x 2 x 3 x 3

Factors of 108 = 2 x 2 x 3 x 3 x 3

LCM = 2 x 2 x 2 x 3 x 3 x 3 = 1458

HCF = 2 x 2 x 3 x 3 = 24

5)

Facors of 306 = 2 x 3 x 3 x 17

Factors of 657 = 3 x 3 x 73

LCM = 2 x 3 x 3 x 17 x 73 = 22338

HCF = 3 x 3 = 9

Explanation: