Q:

How do you find the difference between the greatest common factor and the least common multiple?

A:

To find both the least common multiple and greatest common factor, find the prime factorizations of the numbers. Then put them into a grid and compare and contrast them.

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To find the GCF and LCM, using an example is appropriate. If the two numbers are 3000 and 2500, finding the prime factorizations is the first step. For 2500, the prime factorization is 2500/2 = 1250/2 = 625/5 = 125/5 = 25/5 = 5, so the numbers are 2 x 2 x 5 x 5 x 5 x 5.

For 3000, the prime factorization is 3000/2 = 1500/2 = 750/5 = 150/5 = 30/5 = 6/2 = 3, so the numbers are 2 x 2 x 5 x 5 x 5 x 2 x 3. The next step is to compare the numbers. Both numbers include 2, 2, 5, 5, and 5. For the GCF, multiple 2 x 2 x 5 x 5 x 5 to get 500, which is the GCF.

For the LCM, again line up the prime factorizations, take out the copies, and multiple them together. So, take 2 x 2 x 5 x 5 x 5 x 5 x 2 x 3 to get 15,000. So the GCF is 500 and the LCM is 15,000, meaning the difference between GCF and LCM is 1,000.

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