Mathematics, Operations (+, -, x, /, etc.), Fractions

Grade 5- 8

### Objective

Students learn about multiples, common multiples, least common multiples, and lowest common denominators.

### Directions

Discuss with students the following facts and reminders as they begin this activity.

**Multiples**
A multiple is the product resulting when two or more factors are multiplied by each other.

5 x 4 = 20--The number 20 is a multiple of 4 and 5.

8 x 6 = 48--The number 48 is a multiple of 8 and 6.

The first five multiples of 4 are 4, 8, 12, 16, and 20.

The first five multiples of 3 are 3, 6, 9, 12, and 15.

The first five multiples of 8 are 8, 16, 24, 32, and 40.

**Common Multiples**
A common multiple is a multiple common to two or more different factors.

The number 8 is a common multiple of both 2 and 4.

The number 6 is a common multiple of both 2 and 3.

The number 12 is a common multiple of 2, 3, 4, and 6.

The first six multiples of 6 are 6, 12, 18, 24, 30, and 36.

The first eight multiples of 4 are 4, 8, 12, 16, 20, 24, 28, and 32.

The numbers 12, 24, and 36 are common multiples of both 4 and 6.

The first six multiples of 8 are 8, 16, 24, 32, 40, and 48.

The first four multiples of 12 are 12, 24, 36, and 48.

The numbers 24 and 48 are common multiples of both 8 and 12.

**Least Common Multiple**
The least common multiple (LCM) is the smallest common multiple of two or more factors.

In the examples above, you will find the following:

The least common multiple of 4 and 6 is 12.

The least common multiple of 8 and 12 is 24.

There are many larger common multiples of two factors.

**Lowest Common Denominator**
The least common multiple is used to determine the appropriate denominator for adding unlike fractions. In adding unlike fractions, it is important to find the lowest common denominator of the fractions. This is exactly the same thing as finding the least common multiple of the denominators.

2 6

--- = ---

4 12 The lowest common denominator (LCD)

+ of 4 and 6 is 12.

1 2

--- = ---

6 12

--------------

8 2

--- = ---

12 3

### Resources

- Mighty Multiples activity pages
- pencils