Question

Find the LCM and HCF of the following integers by the prime factorization method.
(1) 12, 15 and 21 (1) 17, 23, and 29 (iii) 8, 9 and 25
2
(iv) 72 and 108
(v) 306 and 657
2, 3, 4
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Answer 1

Answer:

(i). Factors of 12 = 1 × 2 × 2 × 3

Factors of 15 = 1 × 3 × 5

Factors of 21 = 1 × 3 × 7

HCF (12, 15, 21) = 3

LCM (12, 15, 21) = 2 × 2 × 3 × 5 × 7 = 420

(ii). Factors of 17 = 1 × 17

Factors of 23 = 1 × 23

Factors of 29 = 1 × 29

HCF (17, 23, 29) = 1

LCM (17, 23, 29) = 1 × 17 × 23 × 29 = 11339

(iii). Factors of 8 = 1 × 2 × 2 × 2

Factors of 9 = 1 × 3 × 3

Factors of 25 = 1 × 5 × 5

HCF (8, 9, 25) = 1

LCM (8, 9, 25) = 2 × 2 × 2 × 3 × 3 × 5 × 5 = 1800

(iv). Factors of 72 = 1 × 2 × 2 × 2 × 3 × 3

Factors of 108 = 1 × 2 × 2 × 3 × 3 × 3

HCF (72, 108) = 2 x 2 x 3 x 3 = 36

LCM (72, 108) = 2 × 2 × 2 × 3 × 3 × 3 = 216

(v). Factors of 306 = 1 × 2 × 3 × 3 × 17

Factors of 657 = 3 × 3 × 73

HCF (306, 657) = 3 x 3 = 9

LCM (306, 657) = 2 × 3 × 3 × 17 × 73 = 22338