I start our unit on fractions by going over Greatest Common Factor and Least Common Multiple. It seems that no matter how many times we go over what factors of a number are and what multiples of a number are and break apart what it means to find the “greatest common factor” and “least common multiple”, some students still get these mixed up. I try to be super intentional about not saying “GCF” or “LCM” with students very often because I know there is likely at least one student who doesn’t know what those letters stand for -I try to use the vocabulary as much as possible with students instead of acronyms. I want them to know what GCF and LCM mean because they will likely see that other places, but if I say “GCF” I always pair it with “Greatest Common Factor”.

We start with greatest common factor and first review what factors are, and then discuss what it means to find the greatest common factor of two numbers. Once students get a quick review of this, they usually remember doing this in 5th grade. I found this year that the methods my students used as 5th graders to find the greatest common factor were the “rainbow method” and T-charts.

We do a few examples where students use one of those two methods before I put up an example with larger numbers like 192 and 320. Students usually give me the reaction I’m looking for by groaning, and I ask why they’re groaning. They tell me the numbers are big and there’s a lot of factors to list. I then ask if they’d like a more efficient method of finding the greatest common factor and introduce students to what I call the “ladder method” to find the greatest common factor. I think I first heard about it from Sarah here. The high school teachers in my building use this method with polynomials, so I want to introduce it to students.

For practice, I have students write a number on a slip of paper that has many factors. Then students pair up and find the greatest common factor of their numbers. I have them check their answers with Desmos. (Did you know that Desmos can find the greatest common factor of numbers? It will also find the least common multiple.) Then once they’ve checked their answers, they find a new partner.

Then we get into finding the least common multiple of numbers. Again, we review multiples, and how they are different from factors.

(We review the above nearly every day in this unit, so you would think I’ve got how I want to display it on the board for students down pat. This is what I ended up liking the best, although I’m still not sold on how I showed factors.)

Then we talk about what it means to find the least common multiple of two numbers. Students usually start to remember doing this as 5th graders. We do a few examples of this before we talk about how we could use the ladder method to find the least common multiple.

Next comes word problems. I’ve modified this worksheet for practice for students.

Then I have a couple different loop activities that I use depending on when they best fit into the schedule. The first has greatest common factor, least common multiple, and prime factorization, while the second loop activity has greatest common factor, least common multiple, and word problems.

Each activity has 6 problems, which is nice because most groups can finish within a class period. However, it’s not nice for keeping groups small if I want one group per problem. I ended up printing two copies of the activity on different colored paper, and this worked great. Half of my students rotated through one color set while the other half rotated through the other color set.

You can download the files for both activities here.