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LCM & GCF 23644 Views


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Description:

OMG you should totes watch this vid. LOL. It’s all about LCM and GCF… FTW. Least Common Multiple and Greatest Common Factor, here we come. TTYL.

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Transcript

00:04

LCM & GCF, a la Shmoop. Just what are these mysterious acronyms?

00:16

Top-secret government organizations? A new form of textspeak?

00:29

Or perhaps some misplaced Scrabble tiles? Actually, they are abbreviations of mathematical

00:33

concepts. We know -- you were hoping for the secret

00:43

organization thing. LCM is an acronym for Least Common Multiple.

00:51

Let's take a look at that one first. Ooh, not so close. Let's back it up a bit,

00:58

boys. There we go. First we need to talk about what

01:02

a multiple is.

01:05

Say you've got the number 6. A multiple is any number that can result from

01:10

multiplying our given number by any other number.

01:14

For example, you can multiply 6 by 1 to get 6...

01:16

...by 2 to get 12...

01:17

...by 3 to get 18...

01:19

...by 4 to get 24, and so on.

01:21

6, 12, 18 and 24 are all multiples of 6.

01:26

If you want to find the multiples of 8, you can multiply 8 by 1 to get 8...

01:30

...by 2 to get 16...

01:31

...and by 3 to get 24. We could keep going, but we can see you're

01:35

in a hurry. If you want to find the Least Common Multiple

01:41

of 6 and 8, you need to find the smallest number that shares both numbers as factors.

01:47

As you can see, it's unfortunately not as easy as merely multiplying the numbers together.

01:55

GCF, or Greatest Common Factor, is basically the reverse.

02:04

When looking for a GCF, you need to find the largest number that will divide evenly into

02:09

two other numbers. Take the numbers 36 and 48.

02:14

Okay, wiseguy. Put them back. Suppose you are given the numbers 36 and 48.

02:19

What factors do they have in common?

02:21

Well, both numbers are even, so 2 works. 3 is also a factor, as are 4 and 6. But the

02:28

greatest common factor -- the granddaddy of them all -- is 12.

02:34

A good way to find the GCF - rather than by using trial and error - is to first use prime

02:40

factorization. 36 breaks down into 2 times 2 times 3 times

02:46

3. 48 breaks down into 2 times 2 times 2 times

02:51

2 times 3. The numbers that the two have in common are

02:54

two 2's and a three. Multiply those out and voila -- 12.

03:06

Practice finding LCM's and GCF's on your own, and it will pay dividends.

03:14

Just don't let the SITF catch you. Those guys are not to be trifled with.

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