 Least Common Multiples
To add when denominators are different, we first find a common denominator. For a review, see Appendixes A and B. We know, for example, that to add 
and 
, we first look for the least common multiple, LCM. Of both 12 and 30. That number becomes the least common denominator, LCD. To find the LCM of 12 and 30, we factor.
12 = 2 . 2 . 3 ;
30 = 2 . 3 . 5.
The LCM is the number that has 2 as a factor twice, 3 as a factor once, and 5 as a factor once:
LCM = 2 . 2 . 3 . 5 = 60.
FINDING LCMS
To find the LCM, use each factor the greatest number of times that it appears in any one factorization.