Using prime factorization, find the HCF and LCM of (i) 30, 72, 432 (ii) 21, 28, 36, 45

Answers:

(i)

30 = 2 × 3 × 5

72 = 2 × 2 × 2 × 3 × 3 => 2³ × 3²

432 = 2 × 2 × 2 × 2 × 3 × 3 × 3 => 2⁴ × 3³

HCF = 2 × 3

HCF = 6

LCM = 2⁴ × 3³ × 5

LCM = 2160

(ii) 21 = 3 × 7

28 = 2 × 2 × 7 => 2² × 7

36 = 2 × 2 × 3 × 3 => 2² × 3²

45 = 5 × 3 × 3 => 5 × 3²

HCF = 1

LCM = 2² × 3² × 5 × 7

LCM = 1260