Question

What is the Greatest Common Factor (GCF) of 14xy2 and 20xyz?
Select one:
6xyz
2xy
4xyz
6xy

What is the Least Common Multiple (LCM) of the two monomials: 450x2y5 and 3,000x4y3?
Select one:
2xy
30xy
150x^2y^3
9,000x^4y^5

Answer 1

Dear Yolo: I think the best thing to do at this point is to look up "Greatest Common Factor" in your textbook or online, so that you'll know what you're looking for. Then pose another question here if you need to.

Answer 2

To find the GCF, write each quantity in terms of its prime factors:

\[14xy^2 = 2*7*x*y^2\]
\[20xyz = 2*2*5*x*y*z\]
Now multiply together the highest power of each factor that they all have in common. They all have a 2 in common, they all have an x in common, and they all have y in common (but only to the first power, not squared). What do you get if you multiply those things together?

Answer 3

Palmer: That's a nice approach!

Answer 4

For the LCM, start in the same way. When you've factored everything, multiply together the highest power found of each factor.

For example:

\[8xy = 2^3*x*y\]\[5x^2y^3 = 5*x^2*y^3\]\[LCM = 2^3*5*x^2*y^3 = 40x^2y^3\]

Answer 5

ok

Answer 6

What do you get for these two problems? I'll check your answers for you.

Answer 7

To find the GCF, write each quantity in terms of its prime factors:

\[14xy^2 = 2*7*x*y^2\]
\[20xyz = 2*2*5*x*y*z\]
Now multiply together the highest power of each factor that they all have in common. They all have a 2 in common, they all have an x in common, and they all have y in common (but only to the first power, not squared). What do you get if you multiply those things together?

Answer 8

Palmer is right on target. Let's get started: the GCF is the product of the factors that these two expressions have in common: GCF = (2)( ? ) ( ? ).