Least Common Multiple of 75/36, 84/78, 63/69, 96/414

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Know Least Common Multiple of fractions 75/36, 84/78, 63/69, 96/414 quickly i.e. 16800 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.

Least Common Multiple (LCM) of 75/36, 84/78, 63/69, 96/414 is 16800.

LCM(75/36, 84/78, 63/69, 96/414) = 16800

LCM of 75/36, 84/78, 63/69, 96/414

Enter two or more fractions separated by "commas"

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

LCM of:

Least Common Multiple of 75/36,84/78,63/69,96/414

Given numbers are 75/36,84/78,63/69,96/414

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 75,84,63,96

Least Common Multiple of Numerators i.e. LCM of 75,84,63,96 is 50400.

GCF of Denominators means GCF of 36,78,69,414 as per the given fractions.

GCF of 36,78,69,414 is 3 as it is the largest common factor for these numbers.

Lets's calculate LCM of 75,84,63,96

LCM of Fractions 75/36,84/78,63/69,96/414 is 16800

2 75, 84, 63, 96
2 75, 42, 63, 48
3 75, 21, 63, 24
7 25, 7, 21, 8
25, 1, 3, 8

∴ So the LCM of the given numbers is 2 x 2 x 3 x 7 x 25 x 1 x 3 x 8 = 50400

Least Common Multiple of 75,84,63,96 with GCF Formula

Least Common Multiple of 75,84,63,96 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 75,84,63,96 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(75,84,63,96) = 3

common factors(in case of two or more numbers have common factors) = 252

GCF(75,84,63,96) x common factors =3 x 252 = 756

LCM(75,84,63,96) = ( 75 × 84 × 63 × 96 ) / 756

LCM(75,84,63,96) = 38102400 / 756

LCM(75,84,63,96) = 50400


Lets's calculate GCF of 36,78,69,414

3 36, 78, 69, 414
12, 26, 23, 138

∴ So the GCF of the given numbers is 3 = 3

Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 50400/3

Therefore the LCM of Fractions 75/36,84/78,63/69,96/414 is 16800

Greatest Common Factor of 36,78,69,414 By Matching Biggest Common Factor Method

Greatest Common Factor of 36,78,69,414 By Matching Biggest Common Factor Method

Factors of 36

List of positive integer factors of 36 that divides 36 without a remainder.

1,2,3,4,6,9,12,18,36

Factors of 78

List of positive integer factors of 78 that divides 78 without a remainder.

1,2,3,6,13,26,39,78

Factors of 69

List of positive integer factors of 69 that divides 69 without a remainder.

1,3,23,69

Factors of 414

List of positive integer factors of 414 that divides 414 without a remainder.

1,2,3,6,9,18,23,46,69,138,207,414

Greatest Common Factor

We found the factors 36,78,69,414 . The biggest common factor number is the GCF number.
So the greatest common factor 36,78,69,414 is 3.


LCM of Fractions Calculation Examples

Here are some samples of LCM of Fractions calculations.

LCM of Fractions Calculation Examples

Here are some samples of LCM of Fractions calculations.

Frequently Asked Questions on Fractional LCM of 75/36, 84/78, 63/69, 96/414

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 75/36, 84/78, 63/69, 96/414?

Answer: LCM of Numerators as per given numbers 75/36, 84/78, 63/69, 96/414 is

LCM of Numerators i.e. for 75,84,63,96 is 50400

GCF of denominators i.e. for 36,78,69,414 is 3.

Thus, LCM of Fractions is 16800.Finally, LCM of Fractions for 75/36, 84/78, 63/69, 96/414 is 16800.