Least Common Multiple LCM - Free Educational videos for Students in K-12 | Lumos Learning

## Least Common Multiple LCM - Free Educational videos for Students in k-12

#### Least Common Multiple LCM - By tecmath

Transcript
00:01 Good day . Welcome to the Tech Math channel .
00:03 What we're going to be having to get in this
00:04 video is ways of working out the least common multiple
00:08 . Okay . And that is the least common multiple
00:10 . Quite often called the L C M . For
00:13 short or the lowest common multiple . It's the smallest
00:16 common number that a set of numbers will go into
00:19 evenly . So an example , say we were looking
00:22 for the lowest common multiple of three and four would
00:27 be looking for The lowest number that both three and
00:31 4 go into . Okay , so there's some different
00:34 ways of working this out . We're going to start
00:37 with the most simple ways that we're going to move
00:38 up to . Some ways you can work it out
00:40 for some fairly tricky numbers . Okay , So yeah
00:44 , sit back and enjoy . By the way ,
00:46 the lowest are at least common multiple for three and
00:48 four is 12 . And I'll tell you why I
00:50 called multiples that numbers that three goes into a three
00:55 six , nine , 12 15 And keep going for
01:02 we got four i 12 , 1620 . And we're
01:08 looking for the lowest number that both these numbers go
01:12 into 12 . Okay . 12 goes three goes into
01:16 12 4 times and four goes into 12 3 times
01:20 . So this is what that least common multiple is
01:22 . But we're generally not going to do this like
01:25 this . I mean , this is a nice simple
01:27 way . If you know your times tables . Well
01:28 , you might be able to do that straight away
01:30 and do this sort of method . But I'm gonna
01:31 show you some other ways of doing this . So
01:34 we're going to look at right now in this video
01:37 is how to work at the lowest common multiple .
01:39 These common multiple have some easier numbers . Some numbers
01:43 you know that you'll have a fair go doing and
01:46 you probably won't make too many mistakes in the next
01:49 video . I'm gonna be looking how to work it
01:50 out for some fairly diabolical examples . Okay , so
01:53 uh you know that that's something to look forward to
01:56 . Um Now We're gonna be having with that for
01:59 instance now is how do we get the least common
02:01 multiple , lowest common multiple for say 60 and 72
02:05 ? So we're gonna go through a few examples now
02:08 . The way that the method I'm going to show
02:10 you doing this is it's a fairly simple method and
02:14 it's it's a division method . What we do is
02:16 we look for a number that goes into both of
02:18 these . Okay , so number that goes in about
02:21 60 and 72 , A common number is say six
02:24 . Okay , six goes into 60 10 times .
02:27 I can jot that down here . Actually , I
02:29 jot down the town here and six goes into 72
02:33 12 times . So now we look at our 10
02:35 and 12 we think . Is there another number that
02:37 goes into both 10 and 12 ? Okay . That
02:40 we can reduce this further And there is . Okay
02:43 we can reduce by dividing by the # two .
02:46 Okay . You'll see that too goes into 10 Five
02:51 times and it goes into 12 6 times . Now
02:55 is there can we reduce this any further ? This
02:57 fire And the six . Is there a number that
02:58 goes into both of these ? Well there's a number
03:00 that goes into it one but it doesn't reduce it
03:02 so we can't reduce anymore . So what we do
03:05 is we multiply these numbers yeah . All together to
03:11 get our least common multiple . Okay So the numbers
03:15 that we divided by and also the numbers that were
03:18 left at the end a case of six times two
03:21 it's 12 times five , 60 times 6th we get
03:27 our least common multiple which is 360 is the L
03:33 . C . M . So did you get that
03:36 now look really really important that you do reduce these
03:38 numbers as low as possible and that's where I'm also
03:41 going to show this method . Next video how you
03:43 can make sure you do this . Okay . So
03:46 really important that you reduce these numbers as much as
03:49 possible . Now let's have a look at a couple
03:52 more examples . I'll tell you what we'll look at
03:54 one more example and then what we'll do is we'll
03:55 look at how we can do it for where we
03:57 have a big you know say we had um multiple
04:00 numbers . So so we wanted to work out the
04:03 least common multiple . Uh the least common multiple of
04:07 12 and 54 . Okay . All right so we're
04:17 looking for a number that goes into both of these
04:19 . Okay , fairly simple . Once again six goes
04:21 in , six goes into this one two times .
04:25 Okay . Two times and it goes into this 19
04:28 times . Okay . Is there a number that goes
04:31 into both to a nine reducing them further then ?
04:34 You can say no there is not . So we're
04:37 gonna be multiplying we're not even going to get that
04:39 old shape now because we didn't manage to go any
04:41 further . We're going to be multiplying these numbers to
04:45 get our L . C . M . Lowest common
04:47 multiple . Okay so we'll just move that back .
04:52 So six times two is 12 times nine . Our
04:58 lowest common multiple is 100 night . So it's a
05:02 fairly simple way of doing that . And it's really
05:03 useful sometimes when you're doing things with fractions and stuff
05:06 like this to find that all these common multiple .
05:09 But Tell you what I want to show you right
05:11 now . How to do this for if you have
05:13 three numbers . Okay . So what about we go
05:15 through a couple of examples of this ? Uh ,
05:17 you say you had three numbers . What would you
05:18 do say we wanted to find the least common multiple
05:20 of 20 for 12 and eight . Okay . So
05:27 we look once again , it's fairly much the same
05:29 thing . We're looking for a common number that goes
05:30 into both of these . We look for a number
05:33 that goes into both . And you go , Hey
05:34 , for goes in for goes into 24 , goes
05:37 into 20 for What ? six times ? It goes
05:41 into 12 3 times ? And he goes into 82
05:44 times . Okay . Is there a number that we
05:47 can reduce this further with and finally enough . It
05:49 doesn't , it's not a number that has to go
05:51 into all three . I tend to try and find
05:53 one that goes into all three at the start but
05:55 it can be a number that just goes into two
05:56 of them . Okay . So is there a number
05:58 that goes into all three ? Well one does but
06:01 it doesn't reduce but the three goes into both of
06:03 these guys so we can divide by three . Okay
06:09 let's do all right . I said yeah okay I
06:12 did do that , yep . Three . Get confused
06:15 with those numbers . Okay , three guys in the
06:19 six twice and he goes into three once this too
06:25 , we just moved down . Okay we just continue
06:27 it down . We're going to now have a look
06:28 . Is there a number the case into any common
06:31 ones of these ones ? And you can say hey
06:32 basic two goes into this and the case and there's
06:36 two goes into two . So I put the two
06:38 there . it goes into this one once , it
06:42 goes into this one once and this one's been moved
06:45 in , it's not going anywhere and we can't reduce
06:46 this anymore . They're on a one . Okay ?
06:49 Even when we multiple , So we're gonna be multiply
06:50 now these numbers here , in fact , we can
06:55 almost ignore those ones because we multiply by one ,
06:57 that doesn't do anything , does it ? So our
07:00 lowest common multiple is just gonna be four times three
07:02 times two , it's 24 . Okay . Yeah ,
07:09 I'm gonna give you one more example of these .
07:11 Okay , what about I will give you the last
07:16 example here of the lowest common multiple of 16 ,
07:21 uh 24 And 36 . And we want to find
07:25 the least common multiple , lowest common multiple . This
07:28 there you go , number four . Why don't you
07:29 give this one to go ? Okay . There you
07:31 go . You pause that . You came here to
07:33 go . You said four went into this 14 times
07:37 goes into this 16 times goes into this 19 times
07:41 . Okay ? We can reduce either this one or
07:43 this one . So let's choose one . Let's Divide
07:47 two into these two . Numbers , two goes into
07:50 this one twice , goes into this one , throw
07:53 us Okay ? But doesn't go into nine evenly ,
07:56 so we just carry that nine down . Okay ?
07:59 And now we can look and say three goes into
08:02 3 9 . Here , it goes into this one
08:05 Once it goes into this one three times and it
08:10 doesn't get too . So we just moved that to
08:11 down . So there's no common number we can reduce
08:14 these with . So it is going to multiply these
08:16 numbers out . Okay . And that's gonna be the
08:20 numbers we're gonna be multiplying it to get our least
08:23 common mean it makes like an L . So you
08:25 can remember how to do this . Four times two
08:27 is eight times three is 24 Times two is 48
08:34 times three are least common . Mean You got it
08:37 144 . Right ? Hey . That's pretty cool .
08:41 Yeah . Yeah . I'll tell you what , just
08:44 a couple little things with this just to be careful
08:46 of . You have to reduce these numbers down because
08:49 if you only got to this stage You can make
08:51 mistakes . You can get in big problems four times
08:53 6 times four times 9 our least common men would
08:56 not be correct . So you have to reduce these
08:58 right down . But in the next video I'm gonna
09:01 show you a way that you can do this and
09:03 you will always get it right . And I'll tell
09:05 you what the type of example you're gonna get with
09:07 this . In fact , we can work with this
09:09 example . We're going to do next video . We're
09:11 gonna be working at , say , the least common
09:13 means of say nasty diabolical numbers like 5202 and 2431
09:22 . And how you do about doing this . All
09:24 right . So this is something to look forward to
09:27 . And I look forward to seeing you then .
09:28 Anyway . Take care . Hope that video is of
09:30 some help . See you next time . Bye .
Summarizer

#### OVERVIEW:

Least Common Multiple LCM is a free educational video by tecmath.

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