Know Least Common Multiple of fractions 16/30, 24/60, 32/75, 36/120 quickly i.e. 288/15 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.

Least Common Multiple (LCM) of 16/30, 24/60, 32/75, 36/120 is **288/15**.

LCM(16/30, 24/60, 32/75, 36/120) = 288/15

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

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

Given numbers are 16/30,24/60,32/75,36/120

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 16,24,32,36

Least Common Multiple of Numerators i.e. LCM of 16,24,32,36 is 288.

GCF of Denominators means GCF of 30,60,75,120 as per the given fractions.

GCF of 30,60,75,120 is 15 as it is the largest common factor for these numbers.

Lets's calculate LCM of 16,24,32,36

2 | 16, 24, 32, 36 |

2 | 8, 12, 16, 18 |

2 | 4, 6, 8, 9 |

2 | 2, 3, 4, 9 |

3 | 1, 3, 2, 9 |

1, 1, 2, 3 |

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 3 x 1 x 1 x 2 x 3 = 288

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 16,24,32,36 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(16,24,32,36) = 4

common factors(in case of two or more numbers have common factors) = 384

GCF(16,24,32,36) x common factors =4 x 384 = 1536

LCM(16,24,32,36) = ( 16 × 24 × 32 × 36 ) / 1536

LCM(16,24,32,36) = 442368 / 1536

LCM(16,24,32,36) = 288

Lets's calculate GCF of 30,60,75,120

3 | 30, 60, 75, 120 |

5 | 10, 20, 25, 40 |

2, 4, 5, 8 |

∴ So the GCF of the given numbers is 3 x 5 = 15

Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 288/15

Therefore the LCM of Fractions 16/30,24/60,32/75,36/120 is 288/15

**Factors of 30**

List of positive integer factors of 30 that divides 30 without a remainder.

1,2,3,5,6,10,15,30

**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

**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

**Greatest Common Factor**

We found the factors 30,60,75,120 . The biggest common factor number is the **GCF** number.

So the **greatest common factor 30,60,75,120 ** is **15**.

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 16/30, 24/60, 32/75, 36/120?

Answer: LCM of Numerators as per given numbers 16/30, 24/60, 32/75, 36/120 is

LCM of Numerators i.e. for 16,24,32,36 is 288

GCF of denominators i.e. for 30,60,75,120 is 15.

Thus, LCM of Fractions is 288/15.Finally, LCM of Fractions for 16/30, 24/60, 32/75, 36/120 is 288/15.