Least Common Multiple of 31/67, 84/73, 42/21

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Know Least Common Multiple of fractions 31/67, 84/73, 42/21 quickly i.e. 2604 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.

Least Common Multiple (LCM) of 31/67, 84/73, 42/21 is 2604.

LCM(31/67, 84/73, 42/21) = 2604

LCM of 31/67, 84/73, 42/21

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 31/67,84/73,42/21

Given numbers are 31/67,84/73,42/21

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 31,84,42

Least Common Multiple of Numerators i.e. LCM of 31,84,42 is 2604.

GCF of Denominators means GCF of 67,73,21 as per the given fractions.

GCF of 67,73,21 is 1 as it is the largest common factor for these numbers.

Lets's calculate LCM of 31,84,42

LCM of Fractions 31/67,84/73,42/21 is 2604

2 31, 84, 42
3 31, 42, 21
7 31, 14, 7
31, 2, 1

∴ So the LCM of the given numbers is 2 x 3 x 7 x 31 x 2 x 1 = 2604

Least Common Multiple of 31,84,42 with GCF Formula

Least Common Multiple of 31,84,42 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 31,84,42 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(31,84,42) = 1

common factors(in case of two or more numbers have common factors) = 42

GCF(31,84,42) x common factors =1 x 42 = 42

LCM(31,84,42) = ( 31 × 84 × 42 ) / 42

LCM(31,84,42) = 109368 / 42

LCM(31,84,42) = 2604


Lets's calculate GCF of 67,73,21

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

Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 2604/1

Therefore the LCM of Fractions 31/67,84/73,42/21 is 2604

Greatest Common Factor of 67,73,21 By Matching Biggest Common Factor Method

Greatest Common Factor of 67,73,21 By Matching Biggest Common Factor Method

Factors of 67

List of positive integer factors of 67 that divides 67 without a remainder.

1,67

Factors of 73

List of positive integer factors of 73 that divides 73 without a remainder.

1,73

Factors of 21

List of positive integer factors of 21 that divides 21 without a remainder.

1,3,7,21

Greatest Common Factor

We found the factors 67,73,21 . The biggest common factor number is the GCF number.
So the greatest common factor 67,73,21 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 31/67, 84/73, 42/21

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 31/67, 84/73, 42/21?

Answer: LCM of Numerators as per given numbers 31/67, 84/73, 42/21 is

LCM of Numerators i.e. for 31,84,42 is 2604

GCF of denominators i.e. for 67,73,21 is 1.

Thus, LCM of Fractions is 2604.Finally, LCM of Fractions for 31/67, 84/73, 42/21 is 2604.