Uses of Prime Factorization: Finding Least Common Multiple

We continue our exploration of prime factorization.  Any high school math tutor deals with the subject a few times a year.

Continuing from our previous post, let’s investigate one use of the prime factorization:  finding the least common multiple (LCM) of two (or more) numbers.

You can find the LCM just by listing the multiples of the numbers.  For instance, imagine we need the LCM of 12 and 14:

12, 24, 36, 48, 60, 72, 84, 96, 108….

14, 28, 42, 56, 70, 84, ….

We see 84 is the first number to show up in both lists.  Therefore, the LCM of 12 and 14 is 84.

Using the prime factorization method (once again, refer to the previous post for the quick details),



The LCM of 12 and 14 is the simplest combination that includes the prime factorizations of both:


Note that 2x2x3x7 includes the prime factorization of 12 (which is 2x2x3, from above), and also includes the prime factorization of 14 (which is 2×7, also from above).  2×7 does not occur written exactly that way, but since this is multiplication, we could change the order:


Now 2×7 does occur just as written.  Note that 2x2x3x7=2x3x2x7=84, which was the LCM we got from the list method.

This simple trick to find the LCM is very handy as the numbers get bigger.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC


Leave a Reply