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  • What is the least common multiple of 36 and 12?

  • So another way to say this is LCM, in parentheses, 36 to 12.

  • And this is literally saying what's

  • the least common multiple of 36 and 12?

  • Well, this one might pop out at you,

  • because 36 itself is a multiple of 12.

  • And 36 is also a multiple of 36.

  • It's 1 times 36.

  • So the smallest number that is both a multiple of 36 and 12--

  • because 36 is a multiple of 12-- is actually 36.

  • There we go.

  • Let's do a couple more of these.

  • That one was too easy.

  • What is the least common multiple of 18 and 12?

  • And they just state this with a different notation.

  • The least common multiple of 18 and 12

  • is equal to question mark.

  • So let's think about this a little bit.

  • So there's a couple of ways you can think about-- so let's

  • just write down our numbers that we care about.

  • We care about 18, and we care about 12.

  • So there's two ways that we could approach this.

  • One is the prime factorization approach.

  • We can take the prime factorization of both

  • of these numbers and then construct

  • the smallest number whose prime factorization

  • has all of the ingredients of both of these numbers,

  • and that will be the least common multiple.

  • So let's do that.

  • 18 is 2 times 9, which is the same thing as 2 times 3

  • times 3, or 18 is 2 times 9.

  • 9 is 3 times 3.

  • So we could write 18 is equal to 2 times 3 times 3.

  • That's its prime factorization.

  • 12 is 2 times 6.

  • 6 is 2 times 3.

  • So 12 is equal to 2 times 2 times 3.

  • Now, the least common multiple of 18 and 12--

  • let me write this down-- so the least common multiple of 18

  • and 12 is going to have to have enough prime factors to cover

  • both of these numbers and no more,

  • because we want the least common multiple or the smallest

  • common multiple.

  • So let's think about it.

  • Well, it needs to have at least 1, 2, a 3 and a 3

  • in order to be divisible by 18.

  • So let's write that down.

  • So we have to have a 2 times 3 times 3.

  • This makes it divisible by 18.

  • If you multiply this out, you actually get 18.

  • And now let's look at the 12.

  • So this part right over here-- let me make it clear.

  • This part right over here is the part

  • that makes up 18, makes it divisible by 18.

  • And then let's see.

  • 12, we need two 2's and a 3.

  • Well, we already have one 3, so our 3 is taken care of.

  • We have one 2, so this 2 is taken care of.

  • But we don't have two 2s's.

  • So we need another 2 here.

  • So, notice, now this number right over here has a 2 times

  • 2 times 3 in it, or it has a 12 in it, and it has a 2 times

  • 3 times 3, or an 18 in it.

  • So this right over here is the least common multiple

  • of 18 and 12.

  • If we multiply it out, so 2 times 2 is 4.

  • 4 times 3 is 12.

  • 12 times 3 is equal to 36.

  • And we are done.

  • Now, the other way you could've done it

  • is what I would say just the brute force

  • method of just looking at the multiples of these numbers.

  • You would say, well, let's see.

  • The multiples of 18 are 18, 36, and I

  • could keep going higher and higher, 54.

  • And I could keep going.

  • And the multiples of 12 are 12, 24, 36.

  • And immediately I say, well, I don't have to go any further.

  • I already found a multiple of both,

  • and this is the smallest multiple of both.

  • It is 36.

  • You might say, hey, why would I ever do

  • this one right over here as opposed to this one?

  • A couple of reasons.

  • This one, you're kind of-- it's fun,

  • because you're actually decomposing the number

  • and then building it back up.

  • And also, this is a better way, especially if you're

  • doing it with really, really large and hairy numbers.

  • Really, really, really large and hairy numbers

  • where you keep trying to find all the multiples,

  • you might have to go pretty far to actually figure out

  • what their least common multiple is.

  • Here, you'll be able to do it a little bit more systematically,

  • and you'll know what you're doing.

What is the least common multiple of 36 and 12?

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A2 初級 美國腔

最小公倍數練習|因數和倍數|可汗學院|代數預備班 (Least common multiple exercise | Factors and multiples | Pre-Algebra | Khan Academy)

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    gomic88 發佈於 2021 年 01 月 14 日
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