How to solve for lcm and gcf?

Question

mathstudent55 · Answer

Do you know how to get the prime factors of a number?

mathstudent55 · Answer

To get either one, first you must get the prime factors of the numbers.

For example, if you're asked for the LCM and GCF of 54 and 150, first list the prime factors of each number:
54 = 2 x 3 x 3 x 3
or $$54 = 2 \times 3^{3}$$
150 = 2 x 3 x 5 x 5
or $$150 = 2 \times 3 \times 5^{2}$$
To get the LCM, pick common and not common factors with greater exponent. So you pick the 2 bec it's common to both, out of 3^3 and 3 pick 3^3 bec it's common with greater exponent, then also pick the 5^2, so you get LCM = 2 x 2^3 x 5^2

mathstudent55 · Answer

To get the GCF, pick only common factors with the smaller exponent. You pick the 2 bec it's common to both numbers, there is a 3 and a 3^3, so pick the 3. There is a 5 in one number, but not in the other, so it's not common, so don't use it. 
You get GCF = 2 x 3 = 6