Mr. C's Mathemagical Website!
Example 1:
This video is an example of finding the greatest common factor of two monomial expressions.
Example 2:
This is another example. It goes a little further than finding the GCF... it's actually an application of how to use the GCF with a sum of terms, but the first 2:30 of the video is what we're are practicing today.
Example 3:
Here is another video on finding the greatest common factor.
Example 4:
This video is an example of finding the least common multiple. She does a good job explaining the method of how to find an LCM.
FIND THE GCF AND LCM OF 8x2y2 and 20xy3.
To find the GCF of a pair of monomials, write each monomial out as the product of it's prime factors, and then multiply those together.
Since 8 = 4 * 2, and 4 = 2 * 2, the factors of 8 are 2 * 2 * 2, or 23.
x2 can be written as x * x and y2 can be written as y * y.
So, 8x2y2 = 2 * 2 * 2 * x * x * y * y.
20 = 5 * 4, and 4 = 2 * 2, so 20 = 2 * 2 * 5.
y3 = y * y * y.
So, 20xy3 = 2 * 2 * 5 * x * y * y * y.
By looking at both monomials written out, look for any factors they BOTH have. I'm going to make BOLD each factor I see in both.
8x2y2 = 2 * 2 * 2 * x * x * y * y.
20xy3 = 2 * 2 * 5 * x * y * y * y.
The GCF is 2 * 2 * x * y * y = 22xy2 = 4xy2.
To find the least common multiple (LCM), the process is the same, but when you look at your list of all your factors, you want to use the common factors ONCE ONLY. Another way to look at this is to multiply the GCF by everything from both terms we haven't used yet.
8x2y2 = 2 * 2 * 2 * x * x * y * y.
20xy3 = 2 * 2 * 5 * x * y * y * y.
The factors above in RED are the factors we used to find the GREATEST COMMON FACTOR. We will not multoply those by what we haven't used yet (which I have made BLUE) to find the lease common multiple.
The LCM is 4xy2 * 2 * 5 * x * y = 4*2*5*x*x*y2*y = 40x2y3.
If the two monomials don't have any common factors, the GCF is 1.
If the two monomials don't have any common factors, the LCM is the product of the two monomials.
Handouts:
