If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Least common multiple: repeating factors

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?

  • blobby green style avatar for user Carolyn Logan
    how would you find the lcd with letters. For example: x/ab;y/bc;z/ac
    (4 votes)
    Default Khan Academy avatar avatar for user
  • marcimus purple style avatar for user afritz
    what is the least common multiplies of 144 and 38?
    (3 votes)
    Default Khan Academy avatar avatar for user
  • duskpin sapling style avatar for user ja'cara.webb.05
    how is the gcf different from the lcm
    (2 votes)
    Default Khan Academy avatar avatar for user
    • aqualine tree style avatar for user Judith Gibson
      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)
  • purple pi purple style avatar for user Rayyan Asim
    why didnt he add all the three 5's
    (2 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user 21hannahsireginald
    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)
    Default Khan Academy avatar avatar for user
  • aqualine ultimate style avatar for user aiden.cline
    at in the video did he eat
    (2 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user valdespinox
    Does lcm take the highest or lowest exponent?
    (2 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user Cheryl Jones
    What does a whole number with a line over it mean?
    (2 votes)
    Default Khan Academy avatar avatar for user
    • leafers ultimate style avatar for user KathyC
      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)
  • starky sapling style avatar for user juliog16805
    wait so there is not a second stategy
    (1 vote)
    Default Khan Academy avatar avatar for user
    • stelly blue style avatar for user Kim Seidel
      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)
  • blobby green style avatar for user emily suarez
    i dont get in the video at alll
    (3 votes)
    Default Khan Academy avatar avatar for user
    • spunky sam blue style avatar for user L
      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.