Question

lcm of 1800 185 1600​

Answer 1

Solution by Prime Factorization

List all prime factors for each number.

Prime Factorization of 185 is:

5 x 37 => 51 x 371

Prime Factorization of 1600 is:

2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 => 26 x 52

Prime Factorization of 1800 is:

2 x 2 x 2 x 3 x 3 x 5 x 5 => 23 x 32 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, 2, 2, 3, 3, 5, 5, 37

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 x 37 = 532800

In exponential form:

LCM = 26 x 32 x 52 x 371 = 532800

LCM = 532800

Therefore,

LCM(185, 1600, 1800) = 532,800