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 .

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