Question

1. Find the L.C.M. of the following by prime factorisation method.
1. 30, 36
2. 12, 15
3. 5, 7
5. 42, 72
6. 12, 48
7. 60, 75
9. 64, 128
10. 60, 108
78​

Answer 1

Answer:

(i)Prime factorization of the numbers:

30 = 2 × 3 × 5

36 = 2 × 2 × 3 × 3

LCM(30, 36)

= 2 × 2 × 3 × 3 × 5

= 180

(ii)Prime factorization of the numbers:

12 = 2 × 2 × 3

15 = 3 × 5

LCM(12, 15)

= 2 × 2 × 3 × 5

= 60

(iii)Prime factorization of the numbers:

5 = 5

7 = 7

LCM(5, 7)

= 5 × 7

= 35

(iv)Prime factorization of the numbers:

42 = 2 × 3 × 7

72 = 2 × 2 × 2 × 3 × 3

LCM(42, 72)

= 2 × 2 × 2 × 3 × 3 × 7

= 504

(v)Prime factorization of the numbers:

12 = 2 × 2 × 3

48 = 2 × 2 × 2 × 2 × 3

LCM(12, 48)

= 2 × 2 × 2 × 2 × 3

= 48

(vi)Prime factorization of the numbers:

60 = 2 × 2 × 3 × 5

75 = 3 × 5 × 5

LCM(60, 75)

= 2 × 2 × 3 × 5 × 5

= 300

(vii)Prime factorization of the numbers:

64 = 2 × 2 × 2 × 2 × 2 × 2

128 = 2 × 2 × 2 × 2 × 2 × 2 × 2

LCM(64, 128)

= 2 × 2 × 2 × 2 × 2 × 2 × 2

= 128

(viii)Prime factorization of the numbers:

60 = 2 × 2 × 3 × 5

108 = 2 × 2 × 3 × 3 × 3

78 = 2 × 3 × 13

LCM(60, 108, 78)

= 2 × 2 × 3 × 3 × 3 × 5 × 13

= 7020

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