When I first came across the ladder method (ie: the upside-down cake method) for finding greatest common factors and lowest common multiples, I thought it was nothing short of complete genius. This was pretty recent, too! I love learning new methods for teaching math concepts.

Prime factorization is super cool and extremely useful in building number sense, but if the goal is to find GCF and especially LCM, this cake method makes the process so much easier.

Here is a simple video explaining the process:

*relative prime*numbers. In the word wall reference above, LCM= 2x2x2x3x

**10**. While 10 is not prime, it is relatively prime because it and 3 have no more factors in common.

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The cake method is a cool way, however it could become problematic if we try to use it to find LCM for 3 (or more) numbers. Example: LCM of 8, 12, 16 - the cake method will show GCF of 4 with remaining 2, 3, 4 and student will think the LCM is 4x2x3x4=96, but in reality the LCM is 48. Because of that, the prime factorization/factor tree might be safer method. But the cake method will be good if only work with 2 numbers for GCF & LCM. :D

ReplyDeleteYes I came to say the same thing. I only use the cake method for GCF because it works when you need the GCF of 3 numbers but for LCM they need an alternative method anyway so I stick with listing the multiples on the M.

DeleteUNLESS you're like me. I just found out the proper way to use the CAKE METHOD. If you are using 3 numbers-it still works. For example, the LCM of 8,12, 16. I started with dividing them all by 4 which gave me the remainders of 2, 3, 4. YOU CAN DIVIDE ONLY TWO OF THE THREE-WHICH MEANS I CAN DIVIDE THE 2 AND 4, NOT THE 3. IF YOU CAN'T DIVIDE IT, YOU JUST BRING IT DOWN AS A REMAINDER. MIND BLOWN. SO once you do that, you end up with 1, 3 and 2 in your final layer. THEN making the shape of an L would give you 4x2x1x3x2=48. IT DOES WORK EVERYTIME! Hope this helps!

DeleteIt works if you do it in multiple steps - first using 8 and 12 to get an LCM of 24. Then using 24 and 16 to get an LCM of 48. Or you could start with 8 and 16 (16) and then do 16 and 12 to get 48. Or start with 12 and 16 (48) and then do 12 and 48 (still 48).

ReplyDeleteAlternatively, you can do all 3 numbers at once first factoring out everything possible from all 3 numbers, then factoring out anything from 2 numbers and just dropping down the number you didn't divide. In this case after dividing 4 you then chose 2 and get 1, 3, 2 remaining on the bottom. The LCM is 4*2*1*3*2=48 which is the actual LCM. You stop at 4 for the GCF though, that's only the things taken out of all 3 numbers multiplied together. I love this method, it's so amazing!

DeleteMy concern with this method is that it doesn't move them toward algebra readiness. We switch to the prime factorization method so they are ready to apply it to finsing the GCF and LCM of polynomials in their study of rational expressions and equations. Are we going to start teaching the cake method for polynomials also? Otherwise with this easy pass right now, we're setting them up for failure later on.

ReplyDeleteValid concern! The cake method can be used for polynomials, too. I think there's value in showing students that there are multiple ways to approach math problems and that part of their job as students is to find the method that works best for them :)

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