Method A: List each number and the multiples until you come up with a multiple that appears in both of the lists.
Example: Find the LCM of 8 and 12
8: 8, 16, 24, 32, 40, 28, 56, 64, 72, 80
12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120
The LCM for those two numbers is 24 because that is the lowest number that appears in both lists of multiples.
Method B: Make a prime factor tree for each number and then figure out which one has more of each prime number, circle all of that prime number in the one with more, continue with each prime number then multiply all those circled together.
Example: Find the LCM of 8 and 12
8: 2, 2, 2
12: 3, 2, 2
The prime number 2 occurs the most in the factor tree for 8 so I would circle them all and the prime number 3 occurs the most in the factor tree for 12 so I would circle them all. Therefore now I would multiply the numbers I have circled 2x2x2x3 = 24
The girls prefer to use Method B, they say it takes less brain power and is quicker. I never knew Method B existed until I was teaching them how to do it and I have to say I also find it much quicker and easier.
Here's another way too! I like it because it takes less space on the paper, and sometimes the trees run off the edge of the paper if I don't allow enough space.
ReplyDeleteWe write the number and underline it, then draw a perpendicular line straight down, so it looks like a capital T under the number.
If the number is 24, we say "24 divided by 2 (as we write 2 on the left side of the vertical line) is 12 (as we write 12 on the right side of the line).
Then we say 12 divided by 2 is 6 (and write those numbers - the prime 2 on the left, and 6 on the right).
6 divided by 2 is 3 (write 2 and 3)
3 divided by 3 is 1 (write 3 and 1).
When we get to 1, we know we're finished.
Then the numbers on the left are all prime: 2, 2, 2, and 3.
I don't know where we learned this (maybe the one year we did SOS? because BJU teaches trees...), but we've just stuck w/ that method. I looked it up online and can't even find a picture to show you!
I guess I call it a Factor T. (Because a factor box is something else, I think - for factoring trinomials, etc?)
Oh, I do hope you can understand this... lol. =)
I like it... same concept as the factor tree but you're right it takes up far less space! Thanks Marty!
ReplyDeleteYou're welcome!
ReplyDeleteI looked on youtube for a video, but apparently no one else has heard of this method, lol.
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ReplyDeleteOh, and I teach to try the lowest prime numbers first.
ReplyDeleteKeep trying 2 until it will no longer work, then 3, then 5, 7, 11, etc.
This way they are already in order, so when they learn to write them in exponential form, it's handy.
2•2•3•3•3=
2²•3³
http://www.tutornext.com/system/files/u32/Factorization%20of%20168.JPG
ReplyDeleteThat link shows your t-chart method you were talking about. :-) I love how we can live so far apart but yet still help each other out!
Yes! Very cool that we can help each other. =)
ReplyDeleteI do the factor T a little differently, with the 168 on the very top, but this works too!
Whatever doesn't confuse the kids, lol!!!