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The calculator finds all factors of each number by checking all corresponding divisors automatically from 1 to the given number, then it identifies the biggest from the common factors. In this way, the GCF is found. The calculateor uses two inputs to support the GCF and LCM calculation of fractions or ratios (as these are common math exercises). The Least Common Multiple And Greatest Common Factor Calculator will calculate:

- the LCM and GCF of two numbers

**Least Common Multiple And Greatest Common Factor Calculator Parameters:** Numerator and denominator are both integers; the calculator works only for two numbers at once.

The Greatest Common Factor of and (GCF) = | ||||

The Lowest Common Multiple of and (LCM) = | ||||

LCM and GCF Calculations Table | ||||
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LCM formula and calculations | ||||

LCM ( and ) = LCM ( and ) = | ||||

GCF formula and calculations | ||||

GCF ( and ) = GCF ( and ) = | ||||

Least Common Multiple And Greatest Common Factor Calculator Input Values | ||||

Numerator (n) = | ||||

Denominator (d) = |

Please note that the formula for each calculation along with detailed calculations is shown further below this page. As you enter the specific factors of each least common multiple and greatest common factor calculation, the Least Common Multiple And Greatest Common Factor Calculator will automatically calculate the results and update the formula elements with each element of the least common multiple and greatest common factor calculation. You can then email or print this least common multiple and greatest common factor calculation as required for later use.

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All numbers have their own factors (divisors) by which they can be divided. Prime numbers have only two factors: 1 and themselves, while composite numbers have other factors besides these. For example, 7 is a prime number as it is divisible only by 1 and 7, while 8 is a composite number as besides 1 and 8 it is also divisible by 2 and 4. Factors of a number are smaller or equal to the number itself.

Multiples of a number on the other hand, are numbers that are bigger than the original number and all of them share a common property: they are divisible by the original number. For example, 20 is a multiple of 4 because 20 is divisible by 4, while 31 is not a multiple of 7 as 31 is not divisible by 7.

Sometimes we are interested to know the greatest common factor (GCF) of two or more numbers, not just the common factors available. For example, when simplifying fractions, it is more suitable to divide both numerator and denominator by their GCF and write the fraction directly in its lowest terms rather than making a number of consecutive simplifications that are time consuming.

On the other hand, the least common multiple (LCM) is very useful among others when finding the common denominator of two or more fractions with the purpose of adding or subtracting them.

We can find both LCM and GCF of two or more numbers by using the same procedure. Thus, we start dividing the original numbers by prime factors, from the smallest (2) to the biggest possible. If at least one of the numbers is divided by a given prime factor we continue using that prime factor (the number/s that is not divisible with it remains unchanged). This procedure continues until all original numbers become 1.

LCM is then obtained by multiplying all factors used, while GCF is obtained by multiplying only the common factors, as shown in the example below.

Prime Factor | Common Factor | ||
---|---|---|---|

12 | 18 | 2 | 2 |

6 | 9 | 2 | |

3 | 9 | 3 | 3 |

1 | 3 | 3 | |

1 | 1 | 1 | 1 |

Thus, LCM (12 and 18) = 2 × 2 × 3 × 3 × 1 = 36 while for the GCF we multiply only circled numbers, i.e. GCF (12 and 18) = 2 × 3 × 1 = 6.

This calculator presented here carries out the above procedure automatically. All you need to do is insert the input values and the calculator will show you their LCM and GCF without effort.

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The following Math tutorials are provided within the Arithmetic section of our Free Math Tutorials. Each Arithmetic tutorial includes detailed Arithmetic formula and example of how to calculate and resolve specific Arithmetic questions and problems. At the end of each Arithmetic tutorial you will find Arithmetic revision questions with a hidden answer that reveal when clicked. This allows you to learn about Arithmetic and test your knowledge of Math by answering the revision questions on Arithmetic.

- 1.1 - Numbering Systems, a Historical View
- 1.2 - Number Sets, Positive and Negative Numbers and Number Lines
- 1.3 - Operations with Numbers and Properties of Operations
- 1.4 - Order of Operations and PEMDAS Rule
- 1.5 - Multiples, Factors, Prime Numbers and Prime Factorization including LCM and GCF
- 1.6 - Divisibility Rules
- 1.7 - Decimal Number System and Other Numbering Systems

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