LCM & GCF Examples

What's the least common multiple of 20 and 28?

Start by making a list of the multiples of 20:

Now list the multiples of 28:

Since 140 is the smallest multiple that both numbers share, this is the LCM.  

What's the least common multiple of 24 and 36?

This time, we'll go with the second method for finding the LCM. First list the prime factors of both numbers.

The greatest number of times 2 appears is three times (in 24) and the greatest number of times 3 appears is twice (in 36).

So the LCM is .

What's the greatest common factor of 90 and 135?

Let's try Method 2 for the GCF here. First we list the prime factors of both numbers.

We wanna know which factors show up in both lists. Both have two 3s and one 5, so the GCF is:

What's the greatest common factor of 72 and 48?

Method 1 for finding the GCF involves hunting down pairs of factors, so let's do it. The factors of 72 are:

And the factors of 48 are:

The largest factor that they both have in common is 24, so that's our GCF.