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
(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