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Find the LCM and HCF of the following integers by applying the prime factorization method.

(i) 12, 15 and 21

(ii) 17, 23 and 29

(iii) 8, 9 and 25

(iv) 40, 36 and 126

(v) 84, 90 and 12

(vi) 24, 15 and 36

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(i) Prime factors of 12 = 2 × 2 × 3

Prime factors of 15 = 3 × 5

Prime factors of 21 = 3 ×7

Hence LCM of 12, 15 and 21 = 2 × 2 × 3 × 5 × 7 = 420

HCF of 12, 15 and 21 = 3

(ii) Prime factors of 17 = 1 × 17

Prime factors of 23 = 1 ×23

Prime factors of 29 = 1 × 29

Hence LCM of 17, 23 and 29 = 11339

HCF of 17, 23 and 29 = 1

(iii) Prime factors of 8 = 1 × 2 × 2 × 2

Prime factors of 9 = 1 × 3 × 3

Prime factors of 25 = 1 × 5 × 5

Hence LCM of 8, 9 and 25 = 1800

HCF of 8, 9 and 25 = 1

(iv) Prime factors of 40 = 2 × 2 × 2 × 5

Prime factors of 36 = 2 × 2 × 3 × 3

Prime factors of 126 = 2 × 3 × 3 × 7

Hence LCM of 40, 36 and 126 = 2 × 2 × 2 × 3 × 3 × 5 × 7 = 2520

HCF of 40, 36 and 126 = 2

(v) Prime factors of 12 = 2 × 2 × 3

Prime factors of 84 = 2 × 2 × 3 × 7

Prime factors of 90 = 2 × 3 × 3 × 5

Hence LCM of 12, 84 and 90 = 2 × 2 × 3 × 3 × 5 × 7 = 1260

HCF of 12, 84 and 90 = 2 × 3 = 6

(vi) Prime factors of 15 = 3 × 5

Prime factors of 24 = 2 × 2 × 2 × 3

Prime factors of 36 = 2 × 2 × 3 × 3

Hence LCM of 15, 24 and 36 = 2 × 2 × 2 × 3 × 3 × 5 = 360

HCF of 15, 24 and 36 = 3

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