Know Least Common Multiple of fractions 1000/288, 1440/864 quickly i.e. 125 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.

Least Common Multiple (LCM) of 1000/288, 1440/864 is **125**.

LCM(1000/288, 1440/864) = 125

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

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

Given numbers are 1000/288,1440/864

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 1000,1440

Least Common Multiple of Numerators i.e. LCM of 1000,1440 is 36000.

GCF of Denominators means GCF of 288,864 as per the given fractions.

GCF of 288,864 is 288 as it is the largest common factor for these numbers.

Lets's calculate LCM of 1000,1440

2 | 1000, 1440 |

2 | 500, 720 |

2 | 250, 360 |

5 | 125, 180 |

25, 36 |

∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 25 x 36 = 36000

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 1000,1440 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(1000,1440) = 40

common factors(in case of two or more numbers have common factors) = 1

GCF(1000,1440) x common factors =40 x 1 = 40

LCM(1000,1440) = ( 1000 × 1440 ) / 40

LCM(1000,1440) = 1440000 / 40

LCM(1000,1440) = 36000

Lets's calculate GCF of 288,864

2 | 288, 864 |

2 | 144, 432 |

2 | 72, 216 |

2 | 36, 108 |

2 | 18, 54 |

3 | 9, 27 |

3 | 3, 9 |

1, 3 |

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 x 3 x 3 = 288

Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 36000/288

Therefore the LCM of Fractions 1000/288,1440/864 is 125

**Factors of 288**

List of positive integer factors of 288 that divides 288 without a remainder.

1,2,3,4,6,8,9,12,16,18,24,32,36,48,72,96,144,288

**Factors of 864**

List of positive integer factors of 864 that divides 864 without a remainder.

1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,72,96,108,144,216,288,432,864

**Greatest Common Factor**

We found the factors 288,864 . The biggest common factor number is the **GCF** number.

So the **greatest common factor 288,864 ** is **288**.

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 1000/288, 1440/864?

Answer: LCM of Numerators as per given numbers 1000/288, 1440/864 is

LCM of Numerators i.e. for 1000,1440 is 36000

GCF of denominators i.e. for 288,864 is 288.

Thus, LCM of Fractions is 125.Finally, LCM of Fractions for 1000/288, 1440/864 is 125.