# LCM Calculator (Least Common Multiple)

To Calculate the Least Common Multiple of Big Numbers and multiple Variables with steps, Enter your comma-separated variables and choose Method. Press “Calculate” Button.

## What is LCM?

The LCM stands for Least Common Multiple, basically if we have two variables like **x and y**, so **LCM **is a very smallest positive integer which is properly divisible by both **x** and **y** variables.

Suppose, i have 4 and 6 two variables and** the LCM of 4 and 6** will be **12**, here you can see **12** is in both variables’ multiple values as shown below

**Multiple of 4**: (4, 8, **12**, 16, …. )

**Multiple of **6: (6, **12**, 18, …. )

So, I can say that LCM is the smallest number that is divisible by every integer in a given input range of variables.

**Important Note**: *You Must add a comma between variables like 12, 54, 23 as i have added 3 variables. Never add commas inside variable digits like 1,2, 54, 2,3 this will cause error output. because this will make (1), (2), (54), (2), (3) these five variables. instead of 3 as i mentioned above. So Beware while adding input.*

## How To Calculate LCM & Explain It’s Methods?

Using this lcm calculator with variables you can find LCM, i have listed Methods available:

- Prime Factorization Method
- Division Method
- List of multiples

Now i will explain you these methods one by with proper examples to simplify procedure for you for manual calculation.

### How to Find LCM Using Prime Factorization?

In this method we have to find exponent prime factors of each variable and multiply them to carry out LCM.

Let me Show you step by step:

#### Example of Prime factorization Method

Suppose i have taken 14 and 8 as variables to find their prime factors

Prime factors of 14 are ** 2 * 7**

Prime factors of 8 are **2 * 2 * 2**

Now need to pick all factors together but common occurrence of a prime number in both lists should be picked single time.

Final Prime factors List will be like: **2 * 7 * 2 * 2**

Here you can see 2 in 14 is common in both list so i used it once other variables don’t have common instance in both list so i listed them as it is.

So the LCM of 14 and 8 will be multiplication result of Final Prime factors list which is **56**

### How to Find LCM Using List of multiples?

Make a list of each variable multiples until a very smaller number is common in each variable’s list. That will be LCM of those Variables, Let me explain with the help of simple example below

#### Example List of multiples

Suppose more than one variables for example 3 and 9

- list multiples of both 3 and 9 until a common multiple appear in both lists
**Multiples of 3**- 3, 6,
**9,**12, 15, 18, . . . . .

- 3, 6,
**Multiples of 9****9,**18, 27, 36, . . . . .

- Here you can see smallest common number in both list which is
**9** - so
**LCM of 3 and 9**is**9**

### How to Find LCM using Division method?

Using division method we need to divide variables with as much as possible smaller prime number until remainder zero.

#### Example of Division Method

Here using a small example that how division method works to find LCM of 26 and 32

Now i am going to make a division table of both variables to find a list of prime numbers which will determine LCM.

2 | 26 , 32 |

2 | 13 , 16 |

2 | 13 , 8 |

2 | 13 , 4 |

2 | 13 , 2 |

13 | 13 , 1 |

1 , 1 |

Here you can see used the very smallest prime number until I got 1 in the last row but side by side you might noticed that I fetched 13 same in some rows. The reason is 13 is not fully divisibly itself, but other number is divisible by lower prime number than 13 so we should complete other number division which is divisible by lower prime numbers first.

Now List all prime numbers used in division table:

2 * 2 * 2 * 2 * 2 * 13

After multiplication we will get **LCM of 26 and 32** using division method is **416**.

## Important Formula List

Here is some important formula list

Method | Formula |

Least Common Multiple | LCM(a,b) = (a x b) / GCD(a,b) LCM(a,b) = (a x b) / GCF(a,b) LCM(a,b) = (a x b) / HCF(a,b) |

LCM Associative Law | LCM(a, b) = LCM(b, a) |

LCM Commutative Law | LCM(a, b, c) = LCM(LCM(a, b), c) = LCM(a, LCM(b, c)) |

LCM Distributive Law | LCM(da, db, dc) = dLCM(a, b, c) |