Least Common Multiple Trick LCM - Free Educational videos for Students in K-12

Least Common Multiple Trick LCM - By tecmath

Transcript


00:0-1	Good and welcome to the tech mouth channel . What
00:02	we're going to be having a look at in this
00:03	video is a way of working out the least common
00:06	multiple . Now , first off , what is the
00:08	least common multiple ? Well , so we want to
00:10	work out the least common multiple for 72 and 60
00:13	. The least common multiple is the smallest common number
00:17	that these numbers go into . Okay , so We're
00:22	going to have a look at how to do this
00:23	. Now . I have made another video where we
00:25	look at how to make this . This is a
00:26	different method and it's a really good method for working
00:29	at the least common multiple big numbers . And uh
00:32	, it's fairly reliable . In fact , it's 100%
00:34	reliable . So how does this one work ? Now
00:37	? The first thing we're going to do is going
00:38	to find this thing called the greatest common factor .
00:41	And that's the hardest part of this . Doeses't take
00:43	very long . But what the greatest common factor is
00:47	its biggest number that goes into both of these numbers
00:50	. Okay . So to say we were doing this
00:52	the way we do it is we divide the smaller
00:55	of these two numbers into the bigger ones . So
00:57	72 divided by 60 . It's the first step Is
01:01	one with a reminder of 12 . Okay . Yeah
01:05	. Now what we do is we look at the
01:08	remainder here and we're going to carry this on to
01:11	the next stage . So 12 is going to be
01:13	carried on to the next stage . And the smaller
01:16	of these two numbers is also going to be carried
01:18	on to the next stage . It's A 60 and
01:20	12 . And we're going to have a look at
01:23	now . How many times are going to do a
01:25	bit of a repeat ? We divide the smaller of
01:27	these numbers into the large one of these . Okay
01:29	, so 60 divided by 12 . The answer is
01:33	five . Yeah . Put that down and there's no
01:37	reminder . And what this means that there's no reminder
01:41	. This means that 12 I'll give it a circle
01:44	is our greatest common factor . Okay this is the
01:49	biggest number that goes into both 72 and 60 .
01:52	We looked at this in a different video . Did
01:54	Now how can this be used to work out the
01:56	L . C . M . The least common multiple
01:59	. It's as follows . And it's really really simple
02:02	. What we now do Is we divide 12 into
02:05	one of these numbers . This 12 this greatest common
02:08	factor into one either 60 or 72 . Okay so
02:11	I will divide 12 into 72 . 12 in 72
02:15	. It goes six times . Okay six times .
02:19	And what I do is I multiplied by the other
02:22	one . Okay so six times 60 Least common multiple
02:28	is 360 . Okay and it wouldn't have mattered .
02:32	I could have gone uh 60 divided by 12 which
02:34	was five and times it by 72 . And I
02:37	would have got the same answer . Okay So it's
02:40	not about little method for doing this now this is
02:41	a actually a very accurate method to so we'll have
02:46	a look at a couple more examples with this .
02:49	They don't panic straight away if you didn't get that
02:51	straight away . Don't worry . Give you a few
02:53	examples of set you right I'll give you a nice
02:55	easy example to go on with that . We'll have
02:57	a look at right now . So say we wanted
02:59	to work out the uh the L . C .
03:02	M . Of we'll get a nice easy 1 45
03:04	and 20 . And I'm going to put everything in
03:08	order here biggest number smallest number . But if you
03:10	don't have them in that order , you can rearrange
03:12	them so they are . So now what do we
03:13	do first ? We divide the smallest and the largest
03:15	number . 20-45 ? Well , that goes two times
03:19	. Okay ? And there is a remainder . Okay
03:22	? So 45 Divided by 20 is too and there's
03:26	a remainder of five . I moved the remainder across
03:31	now . Okay , So five moves down here and
03:34	the smaller these numbers moved down to the next stage
03:38	, 20 divided by five . Okay , that Goes
03:42	in four times and there's no remainder , so five
03:45	because there's no remainder . Five is our greatest common
03:52	factor . All right . What do we do now
03:55	? We divide this greatest common factor into our two
03:58	original numbers to work out this least common multiple .
04:01	Okay , so 5-45 . Okay , 545 goes nine
04:06	times . Okay , nine many times about 29 times
04:11	20 The L . c . 180 . Pretty cool
04:17	. Right . All right now , you're gonna be
04:19	like , okay that's not necessarily always faster than the
04:22	other method that we looked at in the other video
04:24	. And you correct about this , but it's a
04:25	really great method , especially when you're starting into nasty
04:29	numbers . Okay , what about we do something a
04:32	little bit nastier . What about I do say what's
04:34	the lowest common , the least common multiple of ?
04:38	Okay , lets go nasty here . 1040 And 455
04:45	. Okay , just go a bit crazy . I
04:46	tell you what after this , I'll chuck on an
04:48	even nastier example . So what do we do ,
04:51	divide the smallest into the largest to smallest ? 1040
04:55	, divided by 455 . Okay so this divided by
05:00	this , we're going to get uh two with a
05:05	remainder of 130 array . Okay , So What we
05:12	do is we move this remainder down to the next
05:14	stage . 130 . And I'm gonna move the smaller
05:18	one of these towns . 455 Divided by 130 .
05:23	Okay . How many times has that happened ? Uh
05:26	goes in three times And there is a remainder of
05:30	65 . Okay . Still remind us something that greatest
05:35	common factor yet we'll go one more step , go
05:38	another step . We gotta 65 is going to move
05:40	down the next stage , And 130 is going to
05:43	move down to the next stage is smaller and 20
05:46	130 divided by 65 . Hey , that's two times
05:49	. There's no remainder . So you know what that
05:51	means ? That means we have found our greatest common
05:54	factor which is 65 . Okay this is A .
05:57	G . C . F . Okay so 65 65
06:04	goes into 455 7 times . Okay . 4 55
06:09	divided by 65 is seven um Times by 1000 and
06:13	40 1040 . and uh L . C . M
06:19	. is going to be 7000 280 . See that's
06:27	where this method is really cool for working with ridiculous
06:30	numbers . Okay what about I'm going to give you
06:34	the most nastiest example and most nastiest ? The nastiest
06:37	example . Um That that yeah I thought you might
06:43	actually ever get the case . So what about we
06:45	do the L . C . M . Uh 5,202
06:53	and 2431 . Okay so you know we're gonna do
07:01	we're gonna divide one to the other . Gonna find
07:02	this greatest common factor first . That one goes into
07:05	that one . It goes in it goes in twice
07:10	and there is a reminder of 340 . What about
07:14	your poisons ? And give us a go and see
07:16	. Here you go . I've already started for you
07:18	because it's so here you go . All right ,
07:20	Okay , so we're gonna take the smallest 1 ,
07:22	2431 and I'm going to divide 340 into that .
07:29	Okay , How many times does that occur ? So
07:31	I'm just trying to find a different colour actually .
07:33	It goes in seven times and there's a remainder .
07:37	51 . Okay , um This is what's going to
07:44	happen . 51 is going to move down 340 is
07:48	going to go to the next stage . 340 divided
07:52	by 51 . You're going to get that what ?
07:54	six times Six times . Okay , that's going to
07:58	be 306 is going to be a remainder of 34
08:04	. Okay , keep going . 34 is getting moved
08:09	down 51 . You're gonna see where rapidly getting down
08:12	to the stage . We are we're getting somewhere there
08:15	. Are we gonna go in one time man ?
08:17	Almost right in the wrong pan . One time remained
08:19	uh 17 and 34 . It's going to move to
08:25	this next stage divided by this remainder 17 . It's
08:29	two times two times no remainder . We've got our
08:34	DCF . Okay , the greatest common factor . Okay
08:39	, so I'm going to see how many times this
08:41	goes into one of these numbers . What about 5,202
08:45	divided by 17 . If you do that , you're
08:48	gonna get center of . So this one here divided
08:52	by this one here , You need an answer of
08:54	306 times 2431 . Okay . And what this will
09:06	be if you do this , you'll get this uh
09:09	this least lowest common multiple of 740 . 896 .
09:19	Okay . And yes , I did prepare that one
09:22	earlier . Okay . But I thought I'd show you
09:24	how this method can be used . Okay . Damn
09:28	. What do you think of that method ? I'll
09:29	tell you what it is . 100% accurate . And
09:33	the beauty of it , it means you can if
09:36	you miss out on something on the other method ,
09:38	if you actually don't get it down to its greatest
09:41	common factor , you end up in trouble . But
09:42	this one works all the time anyway . I told
09:46	you think of this . I think it's a great
09:48	method anyway . See you next time . Bye .

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