What is the least common multiple of 18 and 28?

Answer 1

These numbers are not relativly prime, (if they were you could just multiply them and get the answer) and one of them is not a factor of the other, (if it was, the larger number would be the answer,) so you have to make a chart

The multiples of 18 are 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234, 252, and so on

The multiples of 28 are 28, 56, 84, 112, 140, 168, 196, 224, 252, and so on.

As you can see, 252 is the least common multiple, or LCM for short, of 18 and 28

252
252.

First, find the prime factorization of 28 and of 18:

28 = 22 x 7

18 = 2 x 32

To find the least common multiple, each prime factor must be taken the most number of times that it appears in either of the factorizations. Thus, the factor of 2 must be used twice (since 22) appears in the factorization for 28; the factor of 3 must be used twice (since 32) appears in the factorization of 18; and the factor of 7 must be used once (since 7 = 71) appears in the factorization of 28. So the least common multiple of 28 and 18 will be 22 x 32 x 7 = 252.

As another example, to find the least common multiple of 4200 and 8820:

4200 = 23 x 3 x 52 x 7

8820 = 22 x 32 x 5 x 72

So the least common multiple will be 23 x 32 x 52 x 72 = 88200.