What is a Common Multiple? Definition and Examples


What is a common multiple? A common multiple is a multiple that two or more numbers share or have in common. For example, 48 is a common multiple of 6 and 8.

Examples showing how to find the common multiple of two or three numbers


Example #1

Find the common multiple of 6 and 8.

First, list the multiples of each number. In our example here, we will show only the first 13 multiples of each number.

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, ...

Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, ...

As shown in red, the first three common multiples of 6 and 8 are 24, 48, and 72.

Notice that 6 and 8 have a lot more common multiples than just 24, 48, and 72. Just keep listing more and more multiples of each number and you will find more common multiples.

Example #2

Find the common multiple of 5 and 7.

First, list the multiples of each number. In our example here, we will show only the first 16 multiples of each number.

Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, ...

Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, ...

As shown in red, the first two common multiples of 5 and 7 are 35 and 70.

Example #3

Find the common multiple of 2,3 and 4.

First, list the multiples of each number. In our example here, we will show only the first "15" multiples of each number.

Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, ...

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, ...

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, ...

As shown in red, the first two common multiples of 2, 3 and 4 are 12 and 24.

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