# How to use the LCM function

**What is the LCM function?**

The LCM function calculates the least common multiple.

#### Table of Contents

## 1. Introduction

**What is the least common multiplier?**

The least common multiple is the smallest positive integer that is a multiple of all integer arguments.

**When is the LCM function useful?**

Use the LCM function to find fractions with different denominators.

**What is a fraction?**

A fraction has a numerator and a denominator:

- Numerator - The top number in a fraction.
- Denominator - The bottom number.

For example:

6/7

- The numerator is 6, meaning 6 parts.
- The denominator is 7, meaning the whole was split into 7 equal parts.

**How is the least common multiple calculated?**

Finding least common multiples is the product of two numbers divided by their greatest common divisor.

For example,

least common multiple(*number1*,*number2*) = (*number1***number2*) / greatest common divisor(*number1*,*number2*).

least common multiple(6,8) = 6*8/2 = 48/2 = 24

**What is the greatest common divisor?**

The greatest common divisor of two or more integers is the largest integer that divides them all. For two numbers *number1* and *number2*, it is the largest integer that divides both *number1* and *number2* without remainder.

For example:

greatest common divisor(8,12) = 4

This is because 4 is the largest number that divides both 8 and 12.

greatest common divisor(18,24) = 6

6 is the greatest common factor of 18 and 24.

greatest common divisor(10,15,25) = 5

5 is the largest number that divides 10, 15 and 25.

**What is a remainder?**

A remainder is the amount left over after dividing two integers.

The remainder is what is left after dividing two integers. If you divide 15 with 2 you get 7 and 1 is left over. 2*7 equals 14. 15 - 14 equals 1. The remainder is 1.

**What is a divisor?**

A divisor is a number that divides into another number either cleanly or leaving a remainder.

dividend / divisor = quotient( + remainder)

**What is a dividend?**

In division, the dividend is the number being divided.

For example, in the division:

15 / 5 = 3

15 is the dividend 5 is the divisor and 3 is the quotient

**What is a quotient?**

The quotient is the result when two numbers are divided.

**What is a factor?**

A factor is a number that divides evenly into another number, in other words, without leaving a remainder.

**When is the greatest common divisor useful?**

The GCD can be used to reduce fractions to their simplest form. For example, greatest common divisor(36,68) = 4 can simplify 36/68 to 9/17.

**What other Excel functions are about division, dividend, divisor, and quotient?**

Excel Function |
Description |

GCD | Returns the greatest common divisor of two numbers |

LCM | Returns the least common multiple of two numbers |

QUOTIENT | Returns the integer portion of a division between two numbers |

MOD | Returns the remainder after dividing num1 by num2 |

## 2. Syntax

LCM(*number1*, [*number2*], ...)

number1 |
Required. The number you want to calculate the least common multiple for. |

[number2] |
Optional. Up to 254 additional numbers. |

The LCM function returns an error value if any argument is not a number.

## 3. Example

This example demonstrates how to calculate the least common multiple using the LCM function. The image above shows the arguments in cell range B3:C7 and the results in cell range E3:E7.

The first argument pair is 3 and 4 which are displayed in cells B3:C3 respectively. Cell E3 which contains the formula below returns 12. 12 is the least common multiple based on 3 and 4.

Formula in cell E3:

Lets calculate this manually:

First we need to calculate the greatest common divisor.

- Divide a by b and get the quotient q and remainder r, such that a = b * q + r.

a = 4, b = 3

a / b = 1 + 1, q = 1, r = 1 - If r ≠ 0, then greatest common divisor(a, b) = greatest common divisor(b, r), since the greatest common divisor of a and b is the same as the greatest common divisor of b and the remainder r.
- Replace a with b and b with r, and repeat above steps until the remainder becomes 0.

a = 3, b = 1

a/b = 3 + 0, q = 3, r = 0 - If r = 0, then greatest common divisor(a, b) = b, since b is a divisor of a.

greatest common divisor(3, 1) = 1

The greatest common divisor is 1 based on values 4 and 3.

Finding least common multiples is the product of two numbers divided by their greatest common divisor.

least common multiple(*number1*,*number2*) = (*number1***number2*) / greatest common divisor(*number1*,*number2*).

least common multiple(4,3) = 4*3/1 = 12/1 = 12

Our calculated value 12 matches the result in cell E3.

The second argument pair is 24 and 46 which are displayed in cells B4:C4 respectively. Cell E4 which contains the formula below returns 552. 552 is the least common multiple based on 24 and 46.

Formula in cell E4:

Lets calculate this manually:

First we need to calculate the greatest common divisor.

- Divide a by b and get the quotient q and remainder r, such that a = b * q + r.

a = 46, b = 24

a / b = 1 + 22, q = 1, r = 22 - If r ≠ 0, then greatest common divisor(a, b) = greatest common divisor(b, r), since the greatest common divisor of a and b is the same as the greatest common divisor of b and the remainder r.
- Replace a with b and b with r, and repeat above steps until the remainder becomes 0.

a = 24, b = 22

a/b = 1 + 2, q = 1, r = 2 - Replace a with b and b with r, and repeat above steps until the remainder becomes 0.
- a = 22, b = 2

a/b = 11 + 0, q = 11, r = 0 - If r = 0, then greatest common divisor(a, b) = b, since b is a divisor of a.

greatest common divisor(46, 24) = 2

The greatest common divisor is 1 based on values 46 and 24.

Finding least common multiples is the product of two numbers divided by their greatest common divisor.

least common multiple(*number1*,*number2*) = (*number1***number2*) / greatest common divisor(*number1*,*number2*).

least common multiple(46,24) = 46*24/2 = 1104/2 = 552

Our calculated value 552 matches the result in cell E4.

The third argument pair is 12 and 4 which are displayed in cells B5:C5 respectively. Cell E5 which contains the formula below returns 12. 12 is the least common multiple based on 12 and 4.

Formula in cell E4:

Lets calculate this manually:

First we need to calculate the greatest common divisor.

- Divide a by b and get the quotient q and remainder r, such that a = b * q + r.

a = 12, b = 4

a / b = 3 + 0, q = 3, r = 0 - If r = 0, then greatest common divisor(a, b) = b, since b is a divisor of a.

greatest common divisor(12, 4) = 4

The greatest common divisor is 4 based on values 12 and 4.

Finding least common multiples is the product of two numbers divided by their greatest common divisor.

least common multiple(*number1*,*number2*) = (*number1***number2*) / greatest common divisor(*number1*,*number2*).

least common multiple(12,4) = 12*4/4 = 12

Our calculated value 12 matches the result in cell E4.

### Functions in 'Math and trigonometry' category

The LCM function function is one of 62 functions in the 'Math and trigonometry' category.

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