By the time students are in sixth grade, with a little review, they can easily find the greatest common factor or the least common multiple. This is especially true when teachers (and textbooks) give students problems that fall within the parameters set in the Common Core standards.
The standards state that students must be able to determine the GCF of numbers equal or less than 100, and the LCM of numbers up to 12. Keep that in mind before you accidentally ask students to make ridiculously long, tedious lists of factors or multiples!
But working within these parameters, it’s pretty easy for most students to do this.
Except, when they are simply asked to read a word problem and interpret for themselves which of the two is being asked for. Many times, when I give my chapter 1 test, students encounter word problems and take a wild stab at either GCF or LCM, without understanding which one is appropriate in the given situation.
To help solve this problem, I give my students opportunities to practice finding clue words that point to either the GCF or LCM.
By practicing with the real-life terms that one would encounter in GCF or LCM situations, students gain a much better understanding of what is being asked. I have both a practice worksheet and a homework page available as a free download. Check it out!
Another great way to reinforce the idea of GCF vs LCM is to have students complete a hands-on activity that I call Build It! I distribute base-ten rods and cubes, and students practice solving GCF and LCM problems by actually manipulating the items into groups.
For example, students play the role of cafeteria worker, diving peas and carrots equally, forming the greatest number of identical plates. Or they buy packages of baseballs and baseball bats until they have the least possible, common number of both.
I have my students work in pairs or trios to model the situation and perform the correct operation. They enjoy the hands-on approach, and since they are physically creating the solution by dividing (factors) or repeatedly making groups (multiples), they gain an understanding unavailable through the boring old textbook approach.
When they finish, the back of the worksheets allows students the chance to create their own hands-on situations and trade with other groups!
As we review our answers at the end of class, students are actually excited to discuss how they knew if the situation called for finding the GCF or the LCM. How often can we say that?!
Do you have other ways to help your students distinguish between GCF and LCM? I’d love if you left a comment 🙂