I wrote a blog post 2 years ago about using the cake method to find the GCF & LCM of 2 numbers. (I absolutely LOVE this method and my students have had alot of success with it!) I have been meaning to follow up on that post by sharing how to use this method for more than 2 numbers, and since I just got a question about this last week, I figured now is the time to write that post. 🙂

For this example, I will find the greatest common factor & least common multiple of 12, 15, & 18.

Start by writing the 3 numbers next to each other and drawing a “layer of cake” around them. Take out any number that you can divide all three numbers by (in this case 3). Then divide the numbers by 3 and write the quotients under the original numbers, drawing another layer of cake around them. If there is something else you can divide all 3 numbers by, repeat this process. In this case, though, there is nothing (besides 1) that I can divide 4, 5, & 6 by so at this point I like to CHANGE COLORS. Now you need to find if there is any number you can divide *some* of the numbers by. In this case, I can divide 4 and 6 by 2, so I write a 2 on the side (in a different color) and then divide the 4 and 6 by 2. Since I am not dividing the 5 by anything, I just bring it down. Repeat if you can divide some of the numbers by another factor. In this case, I can’t, so I am done.

Find the GCF by multiplying all the numbers on the left that were in the ORIGINAL color ONLY! (In this case, it is only “3”, so my GCF = 3). Find the LCM by multiplying all of the numbers in the “big L” around the cake. (That includes the numbers in both colors). (For this example the LCM = 3 x 2 x 2 x 5 x 3 = 180).

In case my explanation makes no sense, I have included a second example showing this process.

As I said, I absolutely LOVE the cake method and have found that the students love it too and find it MUCH easier than other methods for finding the GCF & LCM. I hope this post helped explain how to use it for more than 2 numbers!

Thanks for reading,

*Christina*

*You also may be interested in my GCF & LCM Halloween Riddle Sheet – available in my TpT store for $1.*