I just went to a workshop and they did this really cool thing with GCF. They called it The Marriage of Two Numbers to find LCM & GCF.
Here's how they did it: They started by saying no wedding is complete without a cake so you need to build the cake with the numbers. I've attached a very primitive example.
We are starting this later this week, so I hope it will work!!
I saw the most amazing youtube or teachertube lesson about prime factorization... then she discussed LCM and GCF too, but cannot find it. Does this sound familiar to anyone? She used a method called "stacks"
I love the stacks method from the video! Thank you so much for sharing. We have already done prime factorization, but I can't honestly say that my students are 100% on the skill. I don't think it would hurt a bit to go back to prime factorization, introduce stacks, and then move along with GCF and LCM. Thanks again for sharing the video!
Sometimes called upside down division. I use this method all the time with my 6th graders. The ladder will do Prime Factorization, GCF, LCM, equivalent fractions and simplifying fractions. I cannot figure out how to link my powerpoint here, so if you would like me to e-mail you a copy of it, e-mail me at firstname.lastname@example.org and I will send it to you.
Good luck with this. It is one of my favorite "tools" that I use all the time.
I teach my sixth graders the ladder method for LCM and GCF. We have come across one set of three numbers that doesn't give you the LCM. Could someone please explain to me why the method doesn't work on this problem?
6,12,15 If you do ladder you get 120 when listing out multiples you get 60. Why the difference?
ok so you can do this method with how many numbers you want... it is the ladder method.
If nothing goes into all three of them its ok! Just do it to the ones that can go into it. Really hard to explain but here's and example....
5| 6 15 <--- (15 can't go into 2, so i just bring it down)
3| 6 3 <---- (6 can't go into 5 either, so I just bring it down)
3| 3 1
3| 1 1 <---- (bring down the 1 because it can't go into three)
1 |1 1
Next times the up! In the case it would be.... *1's are not needed, also!*
2x3x3x3x5 or powers (can't show on my computer)
equals 270! therefore, 270 is the GCF
You made an error and therefore, your answer is incorrect! On line 3/ 6 3 you said that 6 divided by 3 equals 3. It should be 2 of course, and the final answer is 60. While this method is great, your error demeonstrates the danger of using a method but not having a good understanding of the concept. You make a mistake with your method and don't realize that your answer isn't really reasonable. You should know that the LCM of 12 and 15 is 60 and not 270. Oh, and by the way..you are saying you found the GCF...that is greatest common factor. The GCF of 12 and 15 is 3. Sheeesh!
The Ladders Method for 3 (or more) numbers, needs a bit more thought and explanation.
1) When you use it for GCMs you only care about common divisor (or factor) of all 3 (or more) dividends. When you no longer have a common divisor for "ALL" 3 (or more) dividends except 1, you can now safely multiply down the left side of the ladder, to get your GCD (or GCF), while ignoring what's on the bottom line of the ladder.
GCD of 12,15,18?
___4, 5, 6
GCD of 12,15,18 = 3!
2) However, when you use it for LCMs you not only care about common divisor (or factor) of all 3 (or more) dividends, toward the end you process common divisors of a proper subset of the dividend list. When you no longer have a common divisor for "ANY" of the 2 dividends except 1, you can now safely multiply down the left side of the ladder, then multiply across the bottom row of residual dividends (what we teach as multiply the L-pattern) to get your LCM.
3) But in 1 & 2 above, there lies the inconsistency of the method, and the ladders method for GCD vs LCM needs more work. If in a GCD exercise, the student uses the LCM divisor method for "ANY" proper subset of 2 dividends, then their GCD (GCF) multiplication down the left side, will yield an incorrect answer.
GCD of 12,15,18?
3 |12,15,18 "ALL"
2 | 4, 5, 6 "ANY" is WRONG here... must stop when non-1 divisors for "ALL" are found.
___2, 5, 3
GCD of 12,15,18 = 3 x 2 = 6 WRONG!
I teach around this inconsistency, with a HARD STOP in the GCD process after last non-1 divisor is found for ALL number. However in the LCM method upon find all non-1 common divisors for ALL, the students can "creep" some more by extracting non-1 divisors from ANY 2 remaining dividends.
Does anyone have a better way to address the inconsistency?
Personally, I don't like the Cake/Ladder/Stack method all that much in my classroom because it doesn't use the prime factorization that my AZ standards ask for. I love the Venn Diagram method. In this method you use factor trees to find the prime factorization and then you use a Venn diagram to organize them. The things that they have in common will go in the middle section and the things that are not alike will go on the sides. This can also be done for 3 numbers if you use 3 circles. It is easy enough to find the GCF by multiplying all of the numbers in the middle. Then to find the LCM, find the product of all of the numbers. Or one shortcut that we have found in my classes is that if we multiply one of the numbers by the "leftovers" from the other circle, this will give the LCM with a lot less hassle.