Know Least Common Multiple of fractions 6/75, 14/120, 15/200 quickly i.e. 42 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.

Least Common Multiple (LCM) of 6/75, 14/120, 15/200 is **42**.

LCM(6/75, 14/120, 15/200) = 42

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

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

Given numbers are 6/75,14/120,15/200

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 6,14,15

Least Common Multiple of Numerators i.e. LCM of 6,14,15 is 210.

GCF of Denominators means GCF of 75,120,200 as per the given fractions.

GCF of 75,120,200 is 5 as it is the largest common factor for these numbers.

Lets's calculate LCM of 6,14,15

2 | 6, 14, 15 |

3 | 3, 7, 15 |

1, 7, 5 |

∴ So the LCM of the given numbers is 2 x 3 x 1 x 7 x 5 = 210

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 6,14,15 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(6,14,15) = 1

common factors(in case of two or more numbers have common factors) = 6

GCF(6,14,15) x common factors =1 x 6 = 6

LCM(6,14,15) = ( 6 × 14 × 15 ) / 6

LCM(6,14,15) = 1260 / 6

LCM(6,14,15) = 210

Lets's calculate GCF of 75,120,200

5 | 75, 120, 200 |

15, 24, 40 |

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

Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 210/5

Therefore the LCM of Fractions 6/75,14/120,15/200 is 42

**Factors of 75**

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

1,3,5,15,25,75

**Factors of 120**

List of positive integer factors of 120 that divides 120 without a remainder.

1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120

**Factors of 200**

List of positive integer factors of 200 that divides 200 without a remainder.

1,2,4,5,8,10,20,25,40,50,100,200

**Greatest Common Factor**

We found the factors 75,120,200 . The biggest common factor number is the **GCF** number.

So the **greatest common factor 75,120,200 ** 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 6/75, 14/120, 15/200?

Answer: LCM of Numerators as per given numbers 6/75, 14/120, 15/200 is

LCM of Numerators i.e. for 6,14,15 is 210

GCF of denominators i.e. for 75,120,200 is 5.

Thus, LCM of Fractions is 42.Finally, LCM of Fractions for 6/75, 14/120, 15/200 is 42.