Question

find the LCM of 100,135,240​

Answer 1

Answer:

the lcm is 10800

Step-by-step explanation:

List all prime factors for each number.

Prime Factorization of 100 is:

2 x 2 x 5 x 5 => 22 x 52

Prime Factorization of 135 is:

3 x 3 x 3 x 5 => 33 x 51

Prime Factorization of 240 is:

2 x 2 x 2 x 2 x 3 x 5 => 24 x 31 x 51

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, 2, 2, 3, 3, 3, 5, 5

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 = 10800

In exponential form:

LCM = 24 x 33 x 52 = 10800

LCM = 10800

Therefore,

LCM(100, 135, 240) = 10,800

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