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The **least common multiple**, aka lowest common multiple of aka lowest common multiple of two integers a and b is the smallest positive integer that is divisible by both a and b.

The term is usually denoted **lcm(a,b)**.

The easiest way to calculate the least common multiple of two or more integers is using our tool below.

## Least Common Multiple Calculator

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Please note that our app is not limited to two integers;

it employs the associative law lcm(a,lcm(b,c)) = law lcm(lcm(a,b),c).

Likewise important, the lowest common multiple is commutative:

lcm(a,b) = lcm(b,a)

For the sake of completion,

lcm(b,b) = b; Idempotence

lcm(a,gcd(a,b)) = a; Absorption

### What does the Least Common Multiple Mean?

Definition: For two given whole numbers a and b, the LCM is the smallest positive whole number that is divisible by both a and b.

### Example of Least Common Multiple

For example, the lcm of 4 and 6, lcm(4,6) = 12.

Usage: For mathematical operations such as addition, subtraction and comparison with simple fractions, we often employ the lcm of the denominators usually referred to as lowest common denominator.

For example: 1/4 + 1/6 = 3/12 + 2/12 = 5/12.

## How do You Find the Least Common Multiple?

Formula: you may use the greatest common factor (gcf) to determine the lcm of two numbers:

Alternatively, using prime factorization, the lcm is the product of multiplying the highest powers of each number expressed as prime number factorization.

Lcm(4,6) = 2^{2} × 3^{1} = 12.

Ahead is a chart with common values for your convenience.

## Table

The aim of this table is to provide you with frequently searched lcms.

Integer 1 | Integer 2 | LCM |
---|---|---|

12 | 8 | 24 |

6 | 8 | 24 |

5 | 8 | 40 |

8 | 10 | 40 |

15 | 20 | 60 |

8 | 3 | 24 |

8 | 9 | 72 |

8 | 20 | 40 |

8 | 24 | 24 |

15 | 12 | 60 |

10 | 12 | 60 |

10 | 15 | 30 |

3 | 10 | 30 |

15 | 9 | 45 |

14 | 10 | 70 |

14 | 16 | 112 |

20 | 12 | 60 |

15 | 18 | 90 |

24 | 16 | 48 |

10 | 19 | 190 |

15 | 30 | 30 |

22 | 4 | 44 |

14 | 21 | 42 |

24 | 30 | 120 |

6 | 14 | 42 |

Next is the summary of our article.

## Conclusion

Lcm(a,b) = the smallest positive integer that is divisible by both a and b.

This ends our article.

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– Article written by Mark, last updated on August 8th, 2023