Question

Determine the L.C.M of the numbers given below:

(i) 48,60
(ii) 42,63
(iii) 18,17
(iv) 15,30,90
(v) 56,65,85
(vi) 180,384,144
(vii) 108,135,162
(viii) 28,36,45,60

Answer 1

(i) Prime factorisation of 48 = 2 × 2 × 2 × 2 × 3
Prime factorisation of 60 = 2 × 2 × 3 × 5
∴ Required LCM = 2 × 2 × 2 × 2 × 3 × 5 = 240
(ii) Prime factorisation of 42 = 2 × 3 × 7
Prime factorisation of 63 = 3 × 3 × 7
∴ Required LCM = 2 × 3 × 3 × 7 = 126
(iii) Prime factorisation of 18 = 2 × 3 × 3
Prime factorisation of 17 = 17
∴ Required LCM = 2 × 3 × 3 × 17 = 306
(iv) Prime factorisation of 15 = 3 × 5
Prime factorisation of 30 = 2 × 3 × 5
Prime factorisation of 90 = 2 × 3 × 3 × 5
∴ Required LCM = 2 × 3 × 3 × 5 = 90
(v) Prime factorisation of 56 = 2 × 2 × 2 × 7
Prime factorisation of 65 = 5 × 13
Prime factorisation of 85 = 5 × 17
∴ Required LCM = 2 × 2 × 2 × 5 × 7 × 13 × 17 = 61,880
(vi) Prime factorisation of 180 = 2 × 2 × 3 × 3 × 5
Prime factorisation of 384 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3
Prime factorisation of 144 = 2 × 2 × 2 × 2 × 3 × 3
∴ Required LCM = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 5 = 5,760
(vii) Prime factorisation of 108 = 2 × 2 × 3 × 3 × 3
Prime factorisation of 135 = 3 × 3 × 3 × 5
Prime factorisation of 162 = 2 × 3 × 3 × 3 × 3
∴ Required LCM = 2 × 2 × 3 × 3 × 3 × 3 × 5 = 1,620
(viii) Prime factorisation of 28 = 2 × 2 × 7
Prime factorisation of 36 = 2 × 2 × 3 × 3
Prime factorisation of 45 = 3 × 3 × 5
Prime factorisation of 60 = 2 × 2 × 3 × 5
∴ Required LCM = 2 × 2 × 3 × 3 × 5 × 7 = 1,260