Chloe for this problem, try to think of the general equation for area of rectangles to determine the lengths and widths. The answers will be a little out of order.
You know that the first piece has an area of 36x2y3 and the second with 48x3y5. You also know that they have the same lengths but different widths. Because they have a rectangular shape and the equation is l•w, you can divide them to find the sides.
Let's set it up: have A1= 36x2y3 and A2= 48x3y5.
Since the lengths are the same, we can use l for both. W1 can be for A1's width and W2 for A2's width. The division would look like this:
A1/A2 = (l•w1)/(1•w2)
Because l appears in the numerator and denominator, it cancels out leaving you with w1/w2. This is key! It's telling you that if you divide the areas by each other, you will get each area's width. So let's solve:
**hint for length later on: 36 and 48 are divisible by 12**
36x2y3 36 • x2 • y3 3 3
-------- = ------------ = ------- = ------
48x3y5 48 • x3 • y5 4•x•y2 4xy2
Because it was set up as A1/A2, we know that the numerator is w1 and the denominator is w2. Thus the width of A1 is 3 and the width of A2 is 4xy2.
In order to find each area's length, we must find out what was removed from both areas in other words the common factor! So what is the greatest common factor for both widths so that when multiplied, it will equal their respective area's? For each variable, what was taken from both the numerator and denominator of both area's?
I hinted earlier that 36 and 48 are both divisible by 12 so that is part of it since that is the greatest common factor of both numbers. In both widths, x2 and y3 were taken out so all together it means that 12x2y3 was the common factor and therefore the length!
For the least common multiple, think of what is the lowest value among the variables that would be possible to remove from.