What is the LCM of 200 100 and 24?

Answer 1

To find the LCM (Least Common Multiple) of some numbers, we find the prime factorization of each number, and make sure to include each factor in the LCM.

So factoring:

200 = 2 * 2 * 2 * 5 * 5 = 23 * 52.

100 = 2 * 2 * 5 * 5 = 22 * 52.

24 = 2 * 2 * 2 * 3 = 23 * 3.

The greatest power of 2 we need is 23. We also need a 3 and a 52.

Multiplying yields:

23 * 3 * 52 = 600.

A quick check of the other multiples of 200 verifies that neither 200 nor 400 is divisible by 24, so 600 must be the least.