Know Least Common Multiple of fractions 65/75, 30/40, 50/60 quickly i.e. 390 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.

Least Common Multiple (LCM) of 65/75, 30/40, 50/60 is **390**.

LCM(65/75, 30/40, 50/60) = 390

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

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

Given numbers are 65/75,30/40,50/60

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 65,30,50

Least Common Multiple of Numerators i.e. LCM of 65,30,50 is 1950.

GCF of Denominators means GCF of 75,40,60 as per the given fractions.

GCF of 75,40,60 is 5 as it is the largest common factor for these numbers.

Lets's calculate LCM of 65,30,50

2 | 65, 30, 50 |

5 | 65, 15, 25 |

13, 3, 5 |

∴ So the LCM of the given numbers is 2 x 5 x 13 x 3 x 5 = 1950

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 65,30,50 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(65,30,50) = 5

common factors(in case of two or more numbers have common factors) = 10

GCF(65,30,50) x common factors =5 x 10 = 50

LCM(65,30,50) = ( 65 × 30 × 50 ) / 50

LCM(65,30,50) = 97500 / 50

LCM(65,30,50) = 1950

Lets's calculate GCF of 75,40,60

5 | 75, 40, 60 |

15, 8, 12 |

∴ So the GCF of the given numbers is 5 = 5

Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 1950/5

Therefore the LCM of Fractions 65/75,30/40,50/60 is 390

**Factors of 75**

List of positive integer factors of 75 that divides 75 without a remainder.

1,3,5,15,25,75

**Factors of 40**

List of positive integer factors of 40 that divides 40 without a remainder.

1,2,4,5,8,10,20,40

**Factors of 60**

List of positive integer factors of 60 that divides 60 without a remainder.

1,2,3,4,5,6,10,12,15,20,30,60

**Greatest Common Factor**

We found the factors 75,40,60 . The biggest common factor number is the **GCF** number.

So the **greatest common factor 75,40,60 ** is **5**.

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 65/75, 30/40, 50/60?

Answer: LCM of Numerators as per given numbers 65/75, 30/40, 50/60 is

LCM of Numerators i.e. for 65,30,50 is 1950

GCF of denominators i.e. for 75,40,60 is 5.

Thus, LCM of Fractions is 390.Finally, LCM of Fractions for 65/75, 30/40, 50/60 is 390.