Two numbers have prime factorizations of 2 2 • 3 • 5 and 2 • 3 2 • 5. Which expressions will give the greatest common factor and the least common multiple?

Question

 

Two numbers have prime factorizations of 2² • 3 • 5 and 2 • 3²• 5.

Which expressions will give the greatest common factor and the least common multiple?

Answer 1

Two numbers have prime factorizations of 22 • 3 • 5 and 2 • 32 • 5...note 2 squared & 3 squared.

Now, to choose the GCF, you choose, for each base factor in either number, the least exponented one; so the GCF needs a factor 2, a factor 3, and a factor 5. Thus the GCF is 30 (their product). [i.e,2 squared is not a common factor]

To create the LCM, you choose, for each base factor in either number, the greatest exponented one. Thus, LCM needs a factor 2 squared, 3 squared, and 5, giving LCM = 4(9)(5) = 180.