The multiples of a number are all the numbers that are products of the number and any other integer. For example, the multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, and so on.

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**Finding Multiples**

Multiples are found by multiplying the number and any integer.

Example showing the multiples of 3

Multiply 3 by 1, then by 2, then by 3, and so on.

3 x 1 = 3 , 3 x 2 = 6 , 3 x 3 = 9, 3 x 4 = 12 , 3 x 5 = 15 ,

3 x 6 = 18

The first six multiples of 3 are

3 , 6 , 9, 12 , 15 , and 18

You can also find multiples by skip counting. If you can skip count by 3 then you can find the multiples of 3

Example showing the multiples of 5

Multiply 5 by 1, then by 2, then by 3, and so on.

5 x 1 = 5 , 5 x 2 = 10 , 5 x 3 = 15 ,

5 x 4 = 20 , 5 x 5 = 25 , 5 x 6 = 30

The first six multiples of 3 are

5 , 10 , 15, 20 , 25 , and 30

The multiples of 10 are 10, 20, 30, 40, 50, 60 ,and so on

Look for patterns in the multiples of 5 and in the multiples of 10. You might also notice that looking at multiples is just like looking at multiplication (or times) tables.

**Common Multiples**

A Common Multiple is a number that is a multiple of two or more numbers.

To find the Common Multiples of two or more numbers, follow these steps:

- Make a list of multiples for each number
- Continue your list until at least two multiples are common to all lists
- Identify the common multiples

**How to find the Common Multiples**

Follow the three steps below to find common multiples of 6 and 8

List the multiples of 6 | 6, 12, 18 , 24 , 30, 36 , 42 , 48, 54, 60 |

List the multiples of 8 | 8 , 16 , 24 , 32 , 40 , 48 , 56 , 64 |

What are the common multiples? What numbers are multiples of 6 and 8? | 24 and 48 |

Note: We would get more common multiples if we had continued our lists for multiples of 6 and for multiples of 8.

In the example below we will find common multiples for three numbers: 5 , 6 , and 15

List the multiples of 5 | 5 , 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , 60 |

List the multiples of 6 | 6, 12, 18 , 24 , 30, 36 , 42 , 48, 54, 60 |

List the multiples of 15 | 15 , 30 , 45 , 60 , 75 |

What are the common multiples? What numbers are multiples of 5 , 6 ,and 15? | 30 and 60 |

**Common Multiples Worksheet**

- Multiples (1 of 2) (including Least Common Multiple)
- Multiples (2 of 2) (including Least Common Multiple)

**Venn Diagrams**

Venn Diagrams are used to show sets of numbers. Venn Diagrams are really good for showing numbers that belong to more than one set. They do this by having overlapping circles. The example below shows multiples of 5, multiples of 6, and common multiples of 5 and 6.

Multiples of 5 | 5 , 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , 60 |

Multiples of 6 | 6, 12, 18 , 24 , 30, 36 , 42 , 48, 54, 60 |

Common Multiples of 5 and 6 | 30 and 60 |

These multiples of 5 and 6 are shown in the Venn Diagram below. Notice how each set is shown by a circle.

Here are two more sets of numbers shown in a Venn Diagram.

Venn Diagrams can show any sets of numbers or objects.