# Least Common Multiple

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The smallest number among the common multiples of two or more numbers is called their **least common multiple ** (LCM).

* Example: *

Find the LCM of 2, 3 and 6.

* Solution: *

Multiples of 2: 2, 4, **6**, 8, 10, **12**, 14, 16, **18**, ...

Multiples of 3: 3, **6**, 9, **12**, 15, **18**, ...

Multiples of6: **6**, **12**, **18**, ...

The common multiples are 6, 12, 18, ...

The smallest among them is 6.

Therefore, the Least Common Multiple (LCM) is 6.

### Repetitive Division

Using the lists to find the LCM can be slow and tedious. A faster way is to use **repetitive division** to find the least common multiple.

Divide the numbers by prime numbers. If a number cannot be divided it is copied down to the next step of division.

For example, to find the LCM of 3, 6 and 9, we divide them by any factor of the numbers in the following manner:

Least Common Multiple (LCM)

Find the LCM by listing the multiples of each number and find the smallest one that is common.

Another method is to use prime factorization.

The following video shows how to obtain the least common multiple using the repetitive division method.

Finding the LCM of 3 or more numbers

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.