# How to Find the Least Common Multiple (LCM)

## Multiples and Least Common Multiple (LCM)

In this video, I’m going to talk about multiples and the concept of the least common multiple. **To give you an idea of multiple real quick, let’s take multiples of 2.** A multiple of 2 is any number that can be found by multiplying 2 by another integer. 2 has multiples of 2, 4, 6, 8, etc.

**All the even numbers, in fact, all the positive even numbers are multiples of 2.** Multiples of 3 are any number that you can get by multiplying 3 by an integer, so 3, 6, 9, 12, etc. You have all of these sets of numbers that just that go on forever. Where this comes into play is, for instance, if you’re looking for a common denominator between two fractions.

I mentioned this briefly in my video on adding and subtracting fractions, but when you have two fractions and you want to add or subtract them and they have different denominators, you have to find the common denominator before you can add or subtract. In this case, we had 6 and 3.

**In order to get the same denominator on these, we had to find a common denominator.** We’ve already got the multiples of 3 listed out here, but let me give you the multiples of 6 real quick. For 6 we have 6, 12, 18, 24, and so on.

To find the least common denominator, essentially what we’re doing is we’re comparing these two lists and saying, **“What’s the lowest number that appears in both of these lists?”** In this case, it’s 6. 6 appears in both of these lists. This is kind of an easy one, because 6 is just 2 times 3.

Let’s say we had a harder one, like 1/7 and 1/5. To find this, let’s write out the multiples of 5 and 7. With five we have 5, 10, 15, 20, 25, 30, 35, 40, and so on. With 7 we have 7, 14, 21, 28, 35, 42, 49, 56, and so on. In this one, we have to go out a little farther than we did up here.

**Fives are kind of easy, because anything that’s a multiple of 5 is going to either end in 5 or a zero.** We can just look in this list for anything that meets that criterion. This is the first number we find: 35. The least common multiple between 7 and 5 is 35.

That is what we would have to convert the denominator to over here in order to add those two fractions. That’s kind of how multiples can be useful. If you’re dealing with fractions a lot, you’re going to have to do this sort of converting of fractions a lot. This should give you an idea of how to do that.