Least common multiples

Can anyone describe one or more methods of finding least common multiples? I know there is one involved with prime factors or something?

For example, 6,7 and 8's LCM?

6: 2 *......... 3
7:..................7
8: 2 * 2 * 2
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...2 * 2 * 2 * 3 * 7 = 168 = LCM of 6, 7 and 8

LCM = greatest common factors * other factors

6, 7, 8
common --> 2
others -----> 3, 7, 4

LCM = 2 * 3 * 4 * 7 = 168