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Determine the L.C.M of the numbers given below:
(i) 48, 60
Prime factorization of 48 = 2 × 2 × 2 × 2 × 3
Prime factorization of 60 = 2 × 2 × 3 × 5
Therefore, Required LCM = 2 × 2 × 2 × 2 × 3 × 5 = 240
(ii) 42, 63
Prime factorization of 42 = 2 × 3 × 7
Prime factorization of 63 = 3 × 3 × 7
Therefore, Required LCM = 2 × 3 × 3 × 7 = 126
(iii) 18, 17
Prime factorization of 18 = 2 × 3 × 3
Prime factorization of 17 = 17
Therefore, Required LCM = 2 × 3 × 3 × 17 = 306
(iv) 15, 30, 90
Prime factorization of 15 = 3 × 5
Prime factorization of 30 = 2 × 3 × 5
Prime factorization of 90 = 2 × 3 × 3 × 5
Therefore, Required LCM = 2 × 3 × 3 × 5 = 90
(v) 56, 65, 85
Prime factorization of 56 = 2 × 2 × 2 × 7
Prime factorization of 65 = 5 × 13
Prime factorization of 85 = 5 × 17
Therefore, Required LCM = 2 × 2 × 2 × 5 × 7 × 13 × 17 = 61,880
(vi) 180, 384, 144
Prime factorization of 180 = 2 × 2 × 3 × 3 × 5
Prime factorization of 384 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3
Prime factorization of 144 = 2 × 2 × 2 × 2 × 3 × 3
Therefore,
Therefore, Required LCM = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 5 = 5,760
(vii) 108, 135, 162
Prime factorization of 108 = 2 × 2 × 3 × 3 × 3
Prime factorization of 135 = 3 × 3 × 3 × 5
Prime factorization of 162 = 2 × 3 × 3 × 3 × 3
Therefore, Required LCM = 2 × 2 × 3 × 3 × 3 × 3 × 5 = 1,620
(viii) 28, 36, 45, 60
Prime factorization of 28 = 2 × 2 × 7
Prime factorization of 36 = 2 × 2 × 3 × 3
Prime factorization of 45 = 3 × 3 × 5
Therefore, Required LCM =2 × 2 × 3 × 3 × 5 × 7= 1,260
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Chapter 2: Playing With Numbers – Exercise...