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Least Common Multiple (LCM)

Just like GCF's, we can use prime factorizations to find LCM's.  As before, this one is probably at the pre-algebra level.
 

The Prime Factorization Method:

Let's work with numbers that we've already crunched the prime factorizations for...

Find LCM( 24 , 36 )

 

1 )List the prime factorization of each using exponents:

24 = 2^3 x 3 ... 36 = 2^2 x 3^2 ... Line up the bases

2 )Take the larger of each of the exponents...

24 = ( 2^3 ) x 3^1

36 = 2^2 x ( 3^2 )

3 )Multiply these together to get the answer:

 LCM( 24 , 36 ) = 2^3 x 3^2 = 72

Check this using multiple lists!