Question

1. Find the LCM of the following numbers by prime factorization
(a) 12 and 18
(b) 20 and 22
(C) 32 and 48
(d) 55 and 105
(e) 64 and 78
(f) 26,42 and 66
(g) 98, 112 and 144
(h) 48 , 64 and 120
(i) 75,125 and 275
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Answer 1

Find the prime factorization of 12

12 = 2 × 2 × 3

Find the prime factorization of 18

18 = 2 × 3 × 3

Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:

LCM = 2 × 2 × 3 × 3

LCM = 36

Find the prime factorization of 20

20 = 2 × 2 × 5

Find the prime factorization of 22

22 = 2 × 11

Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:

LCM = 2 × 2 × 5 × 11

LCM = 220

Find the prime factorization of 55

55 = 5 × 11

Find the prime factorization of 105

105 = 3 × 5 × 7

Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:

LCM = 3 × 5 × 7 × 11

LCM = 1155

Find the prime factorization of 32

32 = 2 × 2 × 2 × 2 × 2

Find the prime factorization of 48

48 = 2 × 2 × 2 × 2 × 3

Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:

LCM = 2 × 2 × 2 × 2 × 2 × 3

LCM = 96

Find the prime factorization of 64

64 = 2 × 2 × 2 × 2 × 2 × 2

Find the prime factorization of 78

78 = 2 × 3 × 13

Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:

LCM = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 13

LCM = 2496