Question

find the LCM of 45 ,105,and 60, by prime factorization explain please.
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Answer 1

Answer:

Solution by Prime Factorization

List all prime factors for each number.

Prime Factorization of 45 is:

3 x 3 x 5  =>  32 x 51

Prime Factorization of 60 is:

2 x 2 x 3 x 5  =>  22 x 31 x 51

Prime Factorization of 105 is:

3 x 5 x 7  =>  31 x 51 x 71

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 2, 3, 3, 5, 7

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 3 x 3 x 5 x 7 = 1260

In exponential form:

LCM = 22 x 32 x 51 x 71 = 1260

LCM = 1260

Therefore,

LCM(45, 60, 105) = 1260

Step-by-step explanation:

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