## Least Common Multiple

What is a "Multiple" ? The multiples of a number are what you get when you

Here are some examples:

The multiples of

For example, when you write down the multiples of

The multiples of 4 are: 4,8,12,16,

So, the common multiples of 4 and 5 are:

What is the "Least Common Multiple" ? It is simply the

In our previous example, the smallest of the common multiples is

... so the

Finding the Least Common Multiple It is a really easy thing to do. Just start listing the multiples of the numbers until you get a match.

Example: Find the least common multiple for 3 and 5: The multiples of 3 are

and the multiples of 5 are

As you can see on this number line, the first time the multiples match up is 15.

More than 2 Numbers You can also find the least common multiple of 3 (or more) numbers.

Example: Find the least common multiple for 4, 6, and 8 Multiples of 4 are: 4, 8, 12, 16, 20,

Multiples of 6 are: 6, 12, 18,

Multiples of 8 are: 8, 16,

So,

**multiply it by other numbers**(such as if you multiply it by 1,2,3,4,5, etc). Just like the multiplication table.Here are some examples:

The multiples of

**3**are:**3, 6, 9, 12, 15, 18, 21, etc**... The multiples of**12**are:**12, 24, 36, 48, 60, 72, etc...**What is a "Common Multiple" ? When you list the multiples of two (or more) numbers, and find the**same value in both lists**, then that is a*of those numbers.***common multiple**For example, when you write down the multiples of

**4**and**5**, the*common*multiples are those that are found in both lists:The multiples of 4 are: 4,8,12,16,

**20**,24,28,32,36,**40**,44,... The multiples of 5 are: 5,10,15,**20**,25,30,35,**40**,45,50,... Notice that**20**and**40**appear in both lists?So, the common multiples of 4 and 5 are:

**20, 40,**(and 60, 80, etc ..., too)What is the "Least Common Multiple" ? It is simply the

**smallest**of the common multiples.In our previous example, the smallest of the common multiples is

**20**...... so the

**Least**Common Multiple of 4 and 5 is**20**.Finding the Least Common Multiple It is a really easy thing to do. Just start listing the multiples of the numbers until you get a match.

Example: Find the least common multiple for 3 and 5: The multiples of 3 are

**,***3, 6, 9, 12, 15, ...*and the multiples of 5 are

**, like this:***5, 10, 15, 20, ...*As you can see on this number line, the first time the multiples match up is 15.

**Answer: 15**More than 2 Numbers You can also find the least common multiple of 3 (or more) numbers.

Example: Find the least common multiple for 4, 6, and 8 Multiples of 4 are: 4, 8, 12, 16, 20,

**24**, 28, 32, 36, ...Multiples of 6 are: 6, 12, 18,

**24**, 30, 36, ...Multiples of 8 are: 8, 16,

**24**, 32, 40, ....So,

**24**is the least common multiple