Question

find the LCM of 200,140 and 80.​

Answer 1

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Solution by Prime Factorization

List all prime factors for each number.

Prime Factorization of 80 is:

2 x 2 x 2 x 2 x 5 => 2⁴ x 5¹

Prime Factorization of 140 is:

2 x 2 x 5 x 7 => 2² x 5¹ x 7¹

Prime Factorization of 200 is:

2 x 2 x 2 x 5 x 5 => 2³ x 5²

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, 5, 5, 7

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 2 x 2 x 5 x 5 x 7 = 2800

In exponential form:

LCM = 24 x 52 x 71 = 2800

LCM = 2800

Therefore,

LCM(80, 140, 200) = 2800

Answer 2

Answer:

LCM OF 200 IS 10√2

LVM OF 140 IS 42

LCM OF 80 IS 20