Know Least Common Multiple of fractions 45/180, 75/225, 100/270 quickly i.e. 20 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.

Least Common Multiple (LCM) of 45/180, 75/225, 100/270 is **20**.

LCM(45/180, 75/225, 100/270) = 20

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

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

Given numbers are 45/180,75/225,100/270

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 45,75,100

Least Common Multiple of Numerators i.e. LCM of 45,75,100 is 900.

GCF of Denominators means GCF of 180,225,270 as per the given fractions.

GCF of 180,225,270 is 45 as it is the largest common factor for these numbers.

Lets's calculate LCM of 45,75,100

3 | 45, 75, 100 |

5 | 15, 25, 100 |

5 | 3, 5, 20 |

3, 1, 4 |

∴ So the LCM of the given numbers is 3 x 5 x 5 x 3 x 1 x 4 = 900

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 45,75,100 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(45,75,100) = 5

common factors(in case of two or more numbers have common factors) = 75

GCF(45,75,100) x common factors =5 x 75 = 375

LCM(45,75,100) = ( 45 × 75 × 100 ) / 375

LCM(45,75,100) = 337500 / 375

LCM(45,75,100) = 900

Lets's calculate GCF of 180,225,270

3 | 180, 225, 270 |

3 | 60, 75, 90 |

5 | 20, 25, 30 |

4, 5, 6 |

∴ So the GCF of the given numbers is 3 x 3 x 5 = 45

Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 900/45

Therefore the LCM of Fractions 45/180,75/225,100/270 is 20

**Factors of 180**

List of positive integer factors of 180 that divides 180 without a remainder.

1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180

**Factors of 225**

List of positive integer factors of 225 that divides 225 without a remainder.

1,3,5,9,15,25,45,75,225

**Factors of 270**

List of positive integer factors of 270 that divides 270 without a remainder.

1,2,3,5,6,9,10,15,18,27,30,45,54,90,135,270

**Greatest Common Factor**

We found the factors 180,225,270 . The biggest common factor number is the **GCF** number.

So the **greatest common factor 180,225,270 ** is **45**.

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 45/180, 75/225, 100/270?

Answer: LCM of Numerators as per given numbers 45/180, 75/225, 100/270 is

LCM of Numerators i.e. for 45,75,100 is 900

GCF of denominators i.e. for 180,225,270 is 45.

Thus, LCM of Fractions is 20.Finally, LCM of Fractions for 45/180, 75/225, 100/270 is 20.