Question

Find the LCM by prime factorization method 15, 18, 30.​

Answer 1

Answer:

List all prime factors for each number.

Prime Factorization of 12 is:

2 x 2 x 3 => 2^2 x 3^1

Prime Factorization of 18 is:

2 x 3 x 3 => 2^1 x 3^2

Prime Factorization of 30 is:

2 x 3 x 5 => 2^1 x 3^1 x 5^1

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

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 3 x 3 x 5 = 180

In exponential form:

LCM = 2^2 x 3^2 x 5^1 = 180

LCM = 180

Therefore, LCM(12, 18, 30) = 180

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