Well, to find the GCF (Greatest Common Factor) and the LCM (Least Common Multiple) [which uses factoring to find], it makes sense to factor the two expressions (the two monomials). Let’s do that (and we want Prime Factors):

36x

^{2}y^{3}has factors: 2*2*3*3*x*x*y*y*y 48x

^{3}y^{5}has factors: 2*2*2*2*3*x*x*x*y*y*y*y*yFinding the GCF is simply a matter of collecting the common (there’s that word!) factors. Here, they are: 2*2*3*x*x*y*y*y = 12x

^{2}y^{3}Finding the LCM means finding the value that includes all of the factors of the two expressions (with the least number of them possible – there’s that word “least”). Here, it is:

2*2*2*2*3*3*x*x*x*y*y*y*y*y = 144x

^{3}y^{5}(both values divide into this)**Questions A**: The largest possible common length (to have the same length and to get the area of the given expression) is the GCF =

**12x**.

^{2}y^{3}**Question B**:

That means the widths are (all the remaining factors):

**3**because 3 * 12x

^{2}y

^{3}= 36x

^{2}y

^{3}

And 2*2*x*y*y =

**4xy**^{2}because 4xy^{2}* 12x^{2}y^{3}= 48x^{3}y^{5 }^{ }(the original expressions for areas)

**Question C**: (see above)

LCM =

**144x**^{3}y^{5}