Least Common Multiple of 678/12, 384/31, 709/84

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Know Least Common Multiple of fractions 678/12, 384/31, 709/84 quickly i.e. 30764928 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.

Least Common Multiple (LCM) of 678/12, 384/31, 709/84 is 30764928.

LCM(678/12, 384/31, 709/84) = 30764928

LCM of 678/12, 384/31, 709/84

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 678/12,384/31,709/84

Given numbers are 678/12,384/31,709/84

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 678,384,709

Least Common Multiple of Numerators i.e. LCM of 678,384,709 is 30764928.

GCF of Denominators means GCF of 12,31,84 as per the given fractions.

GCF of 12,31,84 is 1 as it is the largest common factor for these numbers.

Lets's calculate LCM of 678,384,709

LCM of Fractions 678/12,384/31,709/84 is 30764928

2 678, 384, 709
3 339, 192, 709
113, 64, 709

∴ So the LCM of the given numbers is 2 x 3 x 113 x 64 x 709 = 30764928

Least Common Multiple of 678,384,709 with GCF Formula

Least Common Multiple of 678,384,709 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 678,384,709 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(678,384,709) = 1

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

GCF(678,384,709) x common factors =1 x 6 = 6

LCM(678,384,709) = ( 678 × 384 × 709 ) / 6

LCM(678,384,709) = 184589568 / 6

LCM(678,384,709) = 30764928


Lets's calculate GCF of 12,31,84

∴ So GCF of numbers is 1 because of no common factors present between them.

Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 30764928/1

Therefore the LCM of Fractions 678/12,384/31,709/84 is 30764928

Greatest Common Factor of 12,31,84 By Matching Biggest Common Factor Method

Greatest Common Factor of 12,31,84 By Matching Biggest Common Factor Method

Factors of 12

List of positive integer factors of 12 that divides 12 without a remainder.

1,2,3,4,6,12

Factors of 31

List of positive integer factors of 31 that divides 31 without a remainder.

1,31

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

Greatest Common Factor

We found the factors 12,31,84 . The biggest common factor number is the GCF number.
So the greatest common factor 12,31,84 is 1.


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 678/12, 384/31, 709/84

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 678/12, 384/31, 709/84?

Answer: LCM of Numerators as per given numbers 678/12, 384/31, 709/84 is

LCM of Numerators i.e. for 678,384,709 is 30764928

GCF of denominators i.e. for 12,31,84 is 1.

Thus, LCM of Fractions is 30764928.Finally, LCM of Fractions for 678/12, 384/31, 709/84 is 30764928.