Two numbers have prime factorizations of 2 2 · 3 · 5 and 2 · 3 2 · 7.

Which expression can be used to find their least common multiple?

... ?

I think for the question above, instead of 2 · 3^2 · 7 it is 2 · 3^2 · 5.

Two numbers have prime factorizations of 2^2 • 3 • 5 and 2 • 3^2 • 5 (note 2 squared & 3 squared).

Now, to choose the GCF, you choose, for each base factor in either number, the least exponent-ed 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.