### LCM Calculator

Aim of LCM Caluclatoe with variables to provide valueable online experience to solve homework and routine assignment work. This is Educational purpose tool for students and Education institutes. Quick and Accurate LCM Results will saves your time and energy.

# What LCM Calculator with Variables is?

The Least Common Multiple is also known as Least Common Divisor or Lowest Common Multiple. Suppose there is two integers 3 and 4, now we have to know about a lowest number which is properly divided by these two numbers. So here 12 is Least Common Multiple / Divisor of 3 and 4, because 12 is divisible by 3 and 4 both.

So, I can say that LCM is smallest number which is divisible by every integer in given comma separated input series.

LCM Calculator with variables have **three calculation methods**:

- How to find LCM using Factorization Method?
- How to find LCM using Division Method?
- How to find LCM List of Multiple Method?

## How to find LCM using Factorization Method?

In this method, we need to follow some steps to get LCM / LCD Results, here is steps listed:

- List out Prime Factors of Each Given Number (Collect all prime numbers as often each occurrence)
- Multiple all collected List of prime numbers to determine LCM.

Note: Same procedure is used for two variables as well as more than two variables, to find prime factors and multiply them together.

**Find LCM( 9 , 12 ) by Prime Factorization – Example**

3 | 9 |

3 | 3 |

1 |

Prime Factors of 9 are **3 × 3**

2 | 12 |

2 | 6 |

3 | 3 |

1 |

Prime Factors of 12 are **2 × 2 ×**

**3**

Here is collective prime factors list is **3 × 3 × 2 × 2** and LCM of 9 and 12 is 36

## How to find LCM using Division Method?

To calculate Least Common Multiple using division method given set of integers set in a cake/ladder way to get one’s at bottom as remainder. at Left side you will get Prime Integers to determine LCM by multiply. Let do an example to learn more about this method theoretically.

**Find LCM( 24 , 30 ) by Division Method – Example**

Here division table of 24 by prime integers, must need to start from as much as lower number can divide target number.

2 | 24 , 30 |

2 | 12 , 15 |

2 | 6 , 15 |

3 | 3 , 15 |

5 | 1 , 5 |

1, 1 |

Here we get List of Prime Integers 2, 2, 2, 3, 5 to find out LCM of 24 and 30, let’s do another step to multiply these values together.

**LCM(24, 30) = 2 × 2 × 2 × 3 × 5 = 120** is Least Common Multiple Answer.

## How to find LCM List of Multiple Method?

In this method, LCM calculator with variables works in a way to expand each variable’s multiples to get a very common smaller integer in every list. Suppose if we have 3 variables and expand their multiple’s list and get lowest X as common value in three lists

Let’s jump into a simple example to understand that concept.

Suppose Find **LCM of 18 and 24** using List of Multiples method

**Multiples of 18** are (18 , 36, 54, **72**, 90, 108)**Multiples of 24** are (24 , 48, **72**, 96, 120)

Here You can see **72** is prominent and its also most smaller common multiple of 18 and 24 multiples list. So, I can write **72 is LCM of 18 and 24**. Its very simple and easy to understand this concept.

### Common Terms Used in LCM Calculator with Variables

Here is some common Or Same terms and abbreviated words list for LCM, let me list down

**HCF**stands for*Highest Common Factor***GCF**stands for*Greatest Common Factor***(GCF Calculator)****GCD**stands for*Greatest Common Divisor***HCM**stands for*Highest Common Measure***GCM**stands for*Greatest Common Measure***HCD**stands for*Highest Common Divisor*

### Formulas Used in LCM Calculator With Variables

Here is some Least Common Multiple from different variables calculation formulas are common. Usually formula needs two variables minimum but for multiple variables we need to use formula recursively. It simple means use answer of each pair to make new pair with next variable until last one.

A set ok very useful, concise and common formulas, you might already know these all.

**Commonly user Formulas for LCM are following:**

LCM via Greatest Common Factor: *LCM(x,y) = x×y / GCF(x,y)*

Distributive LCM: *LCM*(ax,ay,az) = a LCM(x,y,z)

Associative LCM: *LCM(x,y) = LCM(y,x)*

#### Role of Venn Diagrams to find LCM?

Venn Diagrams is visible here as Overlapping circles graph visuals. Basically overlapped region show common data in different data sets. These circular regions took from multiples of two or more variables as dataset. Shaded intersection of data sets is LCM common area. Let me show you as an example image.

Here in this Example suppose A and B two Different data sets of multiples, and C is region of common elements, also we demonstrate for prime factors lists as well.

## Why LCM calculator with variables is useful?

The Least Common Multiple (LCM calculator with variables) calculator is very useful tool for students and educationists. To solve your homework and classwork assignments you can get assistance from this calculator.

It save your time by providing quick results in different required methods by just one click. It operates fully automated and works in batch mode, calculating the output behind the scenes.

Its intelligent and Accurate which makes specific output based on input integers variables. Calculate Prime factors and Make GCD Calculation recursive mode to determine LCM. It’s free of Cost.

**Most Common LCM Searches**

Query | LCM | Detailed Steps |
---|---|---|

lcm of 9 and 12 | 36 | View Step By Step |

lcm of 8 and 14 | 56 | View Step By Step |

lcm of 9 and 15 | 45 | View Step By Step |

lcm of 8 and 12 | 24 | View Step By Step |

lcm of 6 and 9 | 18 | View Step By Step |

lcm of 12 and 15 | 60 | View Step By Step |

lcm of 8 and 10 | 40 | View Step By Step |

lcm of 4 and 6 | 12 | View Step By Step |

lcm of 10 and 12 | 60 | View Step By Step |

lcm of 6 and 12 | 12 | View Step By Step |

lcm of 15 and 20 | 60 | View Step By Step |

lcm of 12 and 18 | 36 | View Step By Step |

lcm of 16 and 20 | 80 | View Step By Step |

lcm of 24 and 30 | 120 | View Step By Step |

lcm of 12 and 16 | 48 | View Step By Step |

lcm of 10 and 28 | 140 | View Step By Step |