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# Least common multiple: repeating factors

CCSS.Math:

To find the Least Common Multiple (LCM) of two integers, follow these steps: 1) Find the prime factorization of both numbers.
2) Determine which prime factors are needed for the least common multiple (LCM) to be divisible by both numbers.
3) Multiply the necessary prime factors together to get the least common multiple (LCM). Created by Sal Khan.

## Want to join the conversation?

- how would you find the lcd with letters. For example: x/ab;y/bc;z/ac(4 votes)
- The denominators use 3 unique factors: a, b and c. None of them occur more than once in any fraction. So, your LCD = abc.

Hope this helps.(0 votes)

- what is the least common multiplies of 144 and 38?(3 votes)
- 144 = 12*12=3*2*2*3*2*2

38=2*19, so since they only have a 2 in common, multiply 144*19 to get the LCM (the 2 in 38 will not repeat).(2 votes)

- how is the gcf different from the lcm(2 votes)
- The gcf is the LARGEST number that WILL DIVIDE INTO both given numbers.

As such, it will be less than at least one (usually both) of the given numbers.

The lcm is the SMALLEST number that BOTH GIVEN NUMBERS DIVIDE into.

As such, it will be greater than at least one (often both) of the given numbers.(2 votes)

- why didnt he add all the three 5's(2 votes)
- when i watched the video, i got confused because i keep trying to do it but i keep getting the answers wrong can you help me more?(2 votes)
- at1:30in the video did he eat(2 votes)
- Does lcm take the highest or lowest exponent?(2 votes)
- The LCM uses the highest exponent.

For example: The LCM for 8x^2 and 12x^3 becomes 24x^3

Hope this helps.(0 votes)

- What does a whole number with a line over it mean?(2 votes)
- I've never seen that notation. But here are some possible meanings:

(1) Someone didn't write a repeating decimal correctly. 6.666666 should be written as 6.6 with a bar or the .6 portion.

(2) Someone forgot to write the top portion of a fraction.

(3) I've read that it can be a VERY rarely used way of indicating "average". So a 3 with a line over it would indicate that 3 is the average of the data set {1,2,3,4,5}.(0 votes)

- wait so there is not a second stategy(1 vote)
- Sal did show an alternative in the prior video: list out the multiples of each number until you find the lowest common multiple of the 2 numbers you are working with. So, you could use that method. Just be aware, it gets very cumbersome if the LCM is a large number. So, its useful that you try to understand the factoring method which Sal demonstrates in this video and the prior video.(2 votes)

- i dont get1:41in the video at alll(3 votes)
- 2 x 3 x 5 = 30, and 5 x 5 = 25.

To get the Least Common Multiple of 30 and 25, you need to know what is the smallest number that both numbers could divide into, so you need to use the factors used to make both numbers. You take the 2 x 3 x 5 of the 30 and one more 5 from the 5 x 5 of the 25.

Then, you have 2 x 3 x 5 x 5, because the factors of 30 already include one of the 5's that the 25 needs to show.

2 x 3 x 5 x 5 = 150, so that is the LCM.

Keep trying, watch the video and others in this section, and look at other people's questions and answers, too. Keep looking and asking and you WILL find an explanation that helps you understand! :-)(0 votes)

## Video transcript

We need to figure out the least
common multiple of 30 and 25. So let's get our little
scratch pad out here. And we care about 30
and we care about 25. And I'm going to do this
using the prime factorization method which I just like more. Let's find the
prime factorization of both of these numbers. So 30, it's divisible by 2. It's 2 times 15. 15 is 3 times 5. And now we've expressed
30 as the product of only prime numbers,
2 times 3 times 5. Now let's do the
same thing for 25. 25 is-- well that's
just 5 times 5. So let me write that down. 25 is equal to 5 times 5. Now to find the least
common multiple, let me write this down,
the least common multiple of 30 and 25 is going to
have a number whose prime factorization is a super
set of both of these or has all of these numbers
in them as many times as we have in any one of these. So it's the least
common multiple. Well it has to be
divisible by 30. So it's going to need a
2 times a 3 times a 5. This is what makes
it divisible by 30. But it needs to also
be divisible by 25. And in order to be
divisible by 25, you need to have two 5s in
your prime factorization. Right now our prime
factorization only has one 5. So let's throw. So we have one 5
right over here. We need another 5. So let's throw another
5 right over here. So now this thing
clearly has a 25 in it. It's clearly divisible by 25. And this is the least
common multiple. I could have, if we just
wanted a common multiple, we could have thrown
more factors here and it would have definitely
been divisible by 30 or 25, but this has the bare
minimum of prime factors necessary to be
divisible by 30 and 25. If I got rid of
any one of these, I wouldn't be divisible
by both anymore. If I got rid of this 2, I
wouldn't be divisible by 30 anymore. If I got rid of one of the 5s,
I wouldn't be divisible by 25 anymore. So let's just multiply it out. This is essentially
the prime factorization of our least common multiple. And this is equal to 2 times 3
is 6, 6 times 5 is 30, 30 times 5 is equal to 150. And of course, we can
check our answer, 150. Check it, and we got it right.