Consider the relationship between greatest common factor and least common multiple.
Let's look at 18 and 12.
The prime factorization of 18 is 2x3x3, and the prime factorization of 12 is 2x2x3. Then, a multiple of 18 that is also a multiple of 12 is 2x2x3x3 [(2x3x3x2 = 18x2) and 2x2x3x3 (2x2x2x3 = 12x3)], or 36.
But, this is just the product of 12 and 18 (216) divided by least common multiple of 12 and 18 (6). 216/6 = 36.
A general method is LCM(a,b) = (axb)/GCF(a,b), and GCF(a,b) = (axb)/LCM(a,b).
This method will be much easier when dealing with polynomials in high school.
9/17/2013

Mark R.