Know Least Common Multiple of fractions 120/14, 180/21, 300/28 quickly i.e. 1800/7 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.

Least Common Multiple (LCM) of 120/14, 180/21, 300/28 is **1800/7**.

LCM(120/14, 180/21, 300/28) = 1800/7

Enter two or more fractions separated by **"commas"**

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

Given numbers are 120/14,180/21,300/28

Formula to find LCM of Fractions is

LCM = LCM of Numerators/GCF of Denominators

As per the formula LCM of Fractions let’s split into two parts and find the LCM of Numerators and GCF of Denominators

In the given fractions LCM of Numerators means LCM of 120,180,300

Least Common Multiple of Numerators i.e. LCM of 120,180,300 is 1800.

GCF of Denominators means GCF of 14,21,28 as per the given fractions.

GCF of 14,21,28 is 7 as it is the largest common factor for these numbers.

Lets's calculate LCM of 120,180,300

2 | 120, 180, 300 |

2 | 60, 90, 150 |

3 | 30, 45, 75 |

5 | 10, 15, 25 |

2, 3, 5 |

∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 2 x 3 x 5 = 1800

The formula of **LCM** is LCM(a_{1},a_{2},a_{3}....,a_{n}) = ( a_{1} × a_{2} × a_{3} × .... × a_{n}) / GCF(a_{1},a_{2},a_{3}....,a_{n}) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 120,180,300 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(120,180,300) = 60

common factors(in case of two or more numbers have common factors) = 60

GCF(120,180,300) x common factors =60 x 60 = 3600

LCM(120,180,300) = ( 120 × 180 × 300 ) / 3600

LCM(120,180,300) = 6480000 / 3600

LCM(120,180,300) = 1800

Lets's calculate GCF of 14,21,28

7 | 14, 21, 28 |

2, 3, 4 |

∴ So the GCF of the given numbers is 7 = 7

Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 1800/7

Therefore the LCM of Fractions 120/14,180/21,300/28 is 1800/7

**Factors of 14**

List of positive integer factors of 14 that divides 14 without a remainder.

1,2,7,14

**Factors of 21**

List of positive integer factors of 21 that divides 21 without a remainder.

1,3,7,21

**Factors of 28**

List of positive integer factors of 28 that divides 28 without a remainder.

1,2,4,7,14,28

**Greatest Common Factor**

We found the factors 14,21,28 . The biggest common factor number is the **GCF** number.

So the **greatest common factor 14,21,28 ** is **7**.

Here are some samples of LCM of Fractions calculations.

1. How to find LCM in Fractions?

Answer: LCM of fractions can be found using the simple formula LCM of Fractions = LCM of Numerators/GCF of Denominators.

2. What is the LCM of Fractions for 120/14, 180/21, 300/28?

Answer: LCM of Numerators as per given numbers 120/14, 180/21, 300/28 is

LCM of Numerators i.e. for 120,180,300 is 1800

GCF of denominators i.e. for 14,21,28 is 7.

Thus, LCM of Fractions is 1800/7.Finally, LCM of Fractions for 120/14, 180/21, 300/28 is 1800/7.