Question

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?
...?

Answer 1

2^2 x 3^2 is the answer... don't be rude and mark the other person bad she gave you a good explanation and fixed your question AND got the answer right... write you question correctly cause you probably just copied it and didn't fix it up!

Just do this for future questions!

Answer 2

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.