# lcm - Least Common Multiple

Concept

lcm is commonly known as least common multiple. When the question asks to find the **lcm**, it's to find the smallest non-zero number that is a multiple of 2 or more numbers. We will be learning the best method of finding lcm in this article.

Let's say we have been asked to find the lcm of 6 and 90. In order to find the LCM of 6 and 90, we first have to find the prime factors of the numbers involved.We can do this through continuous division with prime numbers.

Then we list out the prime factors of each number.

6 = 2 x 3

45 = 3x 3 x 5

To find the lcm, we have to multiply each factor with the largest number of times the factor appears in either number. If the same factor appears more than once in either number, we multiply the factor with the largest number of times it appears.

Prime Factor |
Maximum times factor appears within either number |

2 |
1 |

3 |
2 |

5 |
1 |

Following this method, the LCM of 6 and 45 is 90 (2 x 3 x 3 x 5).

Example

Find the lcm of 4 and 10.

Let us first find the prime factors of each number involved.

4 = 2 x 2

10 = 2 x 5

So we multiply each factor with the largest number of times it appears in either number. The lcm would be 2 x 2 x 5 = 20.

'Try it Yourself' Section

Have you understood our lesson on LCM? If so, please try some of our examples in lcm and test yourself.

a) Find the lcm of 4, 9.

b) Find the lcm of 3, 7, 9.

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