Using Legos to Find LCM

A  4 block and a 6 block.

 As you know, I've been working on ways to use Legos in the high school math classes.  Sometimes, we have to teach skills to students who are supposed to have learned them prior to arriving in high school but didn't for whatever reason.

I've looked at scores for my students and too many are testing in at a 4th, possibly 5th grade level and have managed to get passed grade to grade without the skills.

My pre-algebra class is on their second week of learning LCM because I discovered that too many have been confusing GCF and LCM.

I've tried the fraction strips, listing multiples, factoring trees and many of my students are struggling to learn how to find the LCM.  Some one in elementary taught them something called the butterfly method where they cross multiply the numerator and denominator of two fractions and then multiply the denominators together for the common denominator so they multiply the two numbers together to get the LCM.

My objection to the butterfly method is that it only works if you use two numbers which are some of the smaller numbers or contain a prime such as 4 and 7, otherwise if you have 8 and 4, you end up with a LCM that is too high.  Yes I'm mentioning fractions because LCM and fractions go hand in hand.

I've added Legos to find LCM.

So I pulled out my small set of Legos and started playing with them.  I chose 4 and 6 because those are some of the multiples students have to work with when first learning the process.

First thing I did was lay out a block with 4 circles (a 2 by 2 block) and for 6, I used a four block and a two block to make 6.  You can see it in the first photo.

Second, I added enough four blocks and six blocks until they were exactly the same size as seen in the photo to my left.

They can see they need three 4 blocks and two 6 blocks to get to the lowest common multiple. I think this may provide a better visual than the strips or the butterfly method.

I am hoping they "see" how the numbers relate.  Only time will tell.  Let me know what you think, I'd love to hear.