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

Least Common Multiple - By Anywhere Math

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00:0-1	I always forget . Is it greatest common factor or
00:04	least common factor ? And then is it least common
00:07	multiple or greatest common multiple ? It's really hard to
00:11	keep all these acronyms straight , isn't it ? Welcome
00:32	to anywhere . Math . I'm Jeff , Jacobson .
00:34	And today we're going to add another acronym to the
00:36	list the L . C . M . Or least
00:39	common multiple . Today we're talking about the least common
00:44	multiple or better known as the L . C .
00:47	M . Uh So basically just like greatest common factor
00:51	, the name kind of gives it away . The
00:53	L . C . M . Is just the least
00:54	of the common multiples . You got to remember that
00:58	? We're talking about multiples here . Not factors between
01:02	two or more numbers . There are multiple ways to
01:05	find the L . C . M . Of two
01:07	or more numbers . The first one we're going to
01:09	talk about is doing it by listing multiples . So
01:13	First example find the least common multiple of four and
01:17	6 . And we're going to do it by listing
01:19	multiples when you think multiples ? Think multiply . So
01:23	first , what are the multiples of four or what
01:26	are some of them ? Uh Well four times one
01:29	is for always gonna start out with that . Uh
01:32	Four times two is eight and 12 16 2024 28
01:40	. Uh 32 and so on . We could keep
01:45	going on forever . Next for six . Six times
01:50	one is six and 12 18 24 30 36 42
01:59	. And that's going to keep going on forever .
02:01	Now we want the least common multiple . We've listed
02:08	the multiples . That's the first step . 2nd step
02:10	is to find the ones that are in common .
02:12	So let's find him . Let's circle them . Well
02:16	four and 8 note but there's a 12 in both
02:18	. So that's in common . I'm gonna circle that
02:21	. 16 . No 18 , 20 No 24 .
02:26	Also in common . Uh and then if I keep
02:29	looking there's nothing if I would have gone one more
02:32	here for 36 that also would have been in common
02:35	. Uh but finally , now it's time . What
02:39	is the least of the common multiples ? Well ,
02:42	some common multiples are 12 and 24 and then ,
02:45	But the least is 12 . So the L .
02:49	C . M . or at least come in multiple
02:50	of four and 6 is 12 . Yeah . Let's
02:59	try another problem . Very similar to this . All
03:03	right . Let's look at another problem . So ,
03:05	we're still find the L . C . M .
03:06	By listing multiples . Uh But I'm gonna show you
03:09	a little shortcut and if you understand , it can
03:12	save you a lot of time . So , the
03:14	problem find the l . c . m . of
03:15	six and 14 . Now , you know that the
03:20	L . C . M . Has to be a
03:21	common multiple of both numbers . So we can use
03:26	that information to our advantage and think well 14 is
03:31	the greatest of these numbers . Would it be even
03:35	possible to have a common multiple ? Less than 14
03:39	? And the answer is no right because your first
03:41	multiple for 14 is 14 . So what you do
03:46	is start listing the multiples of your greatest number which
03:51	is 14 in this case . So I'm gonna start
03:53	listing multiples of 14 because I know it would be
03:56	impossible for the L . C . M . to
03:58	be anything less than that . uh so first one
04:01	is 14 Then 28 then 42 and keeps going And
04:08	I'm just gonna check are any of these are common
04:11	multiple with six 14 isn't 28 isn't but 42 is
04:18	. So I know that has to be my least
04:20	common multiple because these two , Yeah . Mhm .
04:25	Didn't work . Yeah but 42 does and it has
04:29	to be common with both . So if it's coming
04:32	here then we're good . So my L . C
04:35	. M . Yeah of six and 14 is 42
04:42	. Okay . Yeah and if you're not quite convinced
04:46	we could still list out All the multiples of six
04:52	until we get up to 42 . So 6 12
04:59	1824 30 36 42 . And notice there's no way
05:05	six or 12 could work because they're less . Right
05:07	? That's what I've mentioned . So those are gone
05:09	immediately . Four or 18 . No 24 . No
05:12	30 no 36 . No 42 . Okay so it's
05:18	very similar to just listing them out but if you
05:21	understand the shortcut it can be a lot quicker .
05:29	For example to we're going to find the L .
05:31	C . M . By prime factor Ization . So
05:35	the first one find the l . c . m
05:36	. of 16 and 20 . So first step is
05:42	to find the prime factor ization of 16 and 20
05:45	. If you want to pause the video , go
05:47	ahead and do that on your own . So The
05:51	prime factor ization of 16 . Uh We could do
05:56	a factor tree but I'm gonna skip that . Um
05:59	It's just basically two times two times two is eight
06:03	Uh Times two is 16 . And we can simplify
06:08	that too . So I'm gonna make that equals as
06:11	well . Uh to to the 4th power . Okay
06:15	, for 20 . Mhm . The prime factor Ization
06:18	is gonna be too Times two , which is four
06:22	Times five , which is 20 . And I can
06:26	simplify that to two squared times five . So those
06:33	are my two prime factories ations Now . Okay .
06:36	From here to find your at least common multiple ,
06:40	all you have to do is circle any unique factors
06:44	. Um So right here , five is unique .
06:48	It's the only one there . So I'm gonna circle
06:50	five . And then you also circle if you have
06:54	common factors between common prime factors between both numbers like
06:59	we do here too . And to uh circle the
07:02	one with the greatest power or the greatest exponent .
07:06	Right ? So in this case I'm not going to
07:09	circle the two squared , I'm going to circle the
07:11	two to the fourth . And then all I'm gonna
07:16	do is multiply those together to get my least common
07:20	multiple . So the least common multiple would then be
07:26	2 to the 4th times five . Yeah to the
07:31	fourth . It's 16 . I already know what that
07:33	is , right . 16 Times five which is 80
07:40	. So my L C . M of 16 and
07:44	20 is 80 . Now you've learned to ways to
07:52	find the least common multiple . We can list multiples
07:55	or we can find it using prime factor Ization .
07:58	Either one will work . Um You also have the
08:01	shortcut . Keep keep that in mind . But there's
08:04	definitely situations where one might be better than the other
08:09	. If your numbers are kind of small , they're
08:11	they're not big numbers like these listing factors can be
08:15	, sorry , listening multiples can be very quick and
08:18	easy . But if you have larger numbers like 16
08:20	or 20 or you have three or four numbers ,
08:24	you don't really want to start listing out all these
08:26	multiples . It's gonna take a long time . So
08:30	as kind of a hint , uh you might want
08:33	to write that down when you have a larger numbers
08:37	. It's good to use prime factor Ization . So
08:42	maybe make a little note to yourself . Good to
08:44	use with larger numbers . Okay , just a little
08:55	hint . And I think that will help out a
08:57	lot . Here's some problems to try in your own
09:00	. Good luck . All right , here's the last
09:06	example for today . Find the L . c .
09:08	m . of three numbers this time . So we're
09:11	gonna find the least common multiple of 4 , 15
09:14	and 18 . If you remember that hint , I
09:17	just mentioned when you've got a lot of numbers .
09:20	Sometimes it's going to save you a lot of time
09:22	to use prime factor Ization . So in this case
09:25	that's what we're gonna do instead of listing out the
09:27	multiples . Uh So real quick again , if you
09:32	want to pause the video and practice your prime factor
09:36	Ization skills , go for it . Go ahead and
09:38	posit uh here we go though . So prime factor
09:42	Ization of of two is just two squared . Prime
09:46	factor Ization of 15 is going to be three times
09:50	five . Those are both prime numbers . Prime factor
09:53	Ization of 18 . Uh Well too , times nine
09:59	is 18 but we can write nine as three square
10:03	, so two times three square . Here's my prime
10:06	factor ization . If you remember from this step ,
10:10	any unique uh prime factors you're gonna circle . If
10:14	it's the only one there , you're gonna circle it
10:16	. So notice five is unique , it's the only
10:20	five there . I'm going to circle that . But
10:21	then when you got comin Prime factors like we've got
10:25	to uh for the four and the 18 and we
10:27	also have three here , circle the one with the
10:30	greatest power or the greatest exploring . So I'm going
10:34	to circle the two squared instead of the two and
10:36	I'm going to circle the three squared here instead of
10:39	the three . My last step is just to multiply
10:45	those together , those things that I circle together .
10:48	So I've got uh I'll say L C M equals
10:53	two squared times three squared times five . Yeah .
11:00	That's gonna be four times 9 times five . Four
11:05	times nine is 36 36 times five is 1 80
11:12	I believe . Let's see . 36 times 51 Yes
11:16	. 1 80 . So my least common multiple of
11:21	4 , 15 and 18 is 1 80 . Yeah
11:28	. Here's some problems that try on your own .
11:35	Thanks for watching this video . And if you liked
11:37	it , please subscribe . Mhm .

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