Least Common Multiple of 78/84, 89/78, 40/314

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Know Least Common Multiple of fractions 78/84, 89/78, 40/314 quickly i.e. 69420 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.

Least Common Multiple (LCM) of 78/84, 89/78, 40/314 is 69420.

LCM(78/84, 89/78, 40/314) = 69420

LCM of 78/84, 89/78, 40/314

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 78/84,89/78,40/314

Given numbers are 78/84,89/78,40/314

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 78,89,40

Least Common Multiple of Numerators i.e. LCM of 78,89,40 is 138840.

GCF of Denominators means GCF of 84,78,314 as per the given fractions.

GCF of 84,78,314 is 2 as it is the largest common factor for these numbers.

Lets's calculate LCM of 78,89,40

LCM of Fractions 78/84,89/78,40/314 is 69420

2 78, 89, 40
39, 89, 20

∴ So the LCM of the given numbers is 2 x 39 x 89 x 20 = 138840

Least Common Multiple of 78,89,40 with GCF Formula

Least Common Multiple of 78,89,40 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 78,89,40 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(78,89,40) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(78,89,40) x common factors =1 x 2 = 2

LCM(78,89,40) = ( 78 × 89 × 40 ) / 2

LCM(78,89,40) = 277680 / 2

LCM(78,89,40) = 138840


Lets's calculate GCF of 84,78,314

2 84, 78, 314
42, 39, 157

∴ So the GCF of the given numbers is 2 = 2

Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 138840/2

Therefore the LCM of Fractions 78/84,89/78,40/314 is 69420

Greatest Common Factor of 84,78,314 By Matching Biggest Common Factor Method

Greatest Common Factor of 84,78,314 By Matching Biggest Common Factor Method

Factors of 84

List of positive integer factors of 84 that divides 84 without a remainder.

1,2,3,4,6,7,12,14,21,28,42,84

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 314

List of positive integer factors of 314 that divides 314 without a remainder.

1,2,157,314

Greatest Common Factor

We found the factors 84,78,314 . The biggest common factor number is the GCF number.
So the greatest common factor 84,78,314 is 2.


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 78/84, 89/78, 40/314

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 78/84, 89/78, 40/314?

Answer: LCM of Numerators as per given numbers 78/84, 89/78, 40/314 is

LCM of Numerators i.e. for 78,89,40 is 138840

GCF of denominators i.e. for 84,78,314 is 2.

Thus, LCM of Fractions is 69420.Finally, LCM of Fractions for 78/84, 89/78, 40/314 is 69420.