ShmoopTube
Where Monty Python meets your 10th grade teacher.
Search Thousands of Shmoop Videos
LCM & GCF 23649 Views
Share It!
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.
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.
Full Transcript
- 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.
Up Next
It's impressive that these expressions are able to stay so rational even when they're having operations performed on them.
Related Videos
Jack and Jill went up the hill to fetch a pail of water. But what happened when they got up there? They’ve been gone an awfully long time…
Sometimes, we just want fewer y's...or more x's. That's why it's great to know how to add and subtract variables. In real life, though, we try to a...