Least Common Multiple of 42/78, 27/30, 21/820

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023


Know Least Common Multiple of fractions 42/78, 27/30, 21/820 quickly i.e. 189 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.

Least Common Multiple (LCM) of 42/78, 27/30, 21/820 is 189.

LCM(42/78, 27/30, 21/820) = 189

LCM of 42/78, 27/30, 21/820

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 42/78,27/30,21/820

Given numbers are 42/78,27/30,21/820

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 42,27,21

Least Common Multiple of Numerators i.e. LCM of 42,27,21 is 378.

GCF of Denominators means GCF of 78,30,820 as per the given fractions.

GCF of 78,30,820 is 2 as it is the largest common factor for these numbers.

Lets's calculate LCM of 42,27,21

LCM of Fractions 42/78,27/30,21/820 is 189

3 42, 27, 21
7 14, 9, 7
2, 9, 1

∴ So the LCM of the given numbers is 3 x 7 x 2 x 9 x 1 = 378

Least Common Multiple of 42,27,21 with GCF Formula

Least Common Multiple of 42,27,21 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 42,27,21 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(42,27,21) = 3

common factors(in case of two or more numbers have common factors) = 21

GCF(42,27,21) x common factors =3 x 21 = 63

LCM(42,27,21) = ( 42 × 27 × 21 ) / 63

LCM(42,27,21) = 23814 / 63

LCM(42,27,21) = 378


Lets's calculate GCF of 78,30,820

2 78, 30, 820
39, 15, 410

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

Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 378/2

Therefore the LCM of Fractions 42/78,27/30,21/820 is 189

Greatest Common Factor of 78,30,820 By Matching Biggest Common Factor Method

Greatest Common Factor of 78,30,820 By Matching Biggest Common Factor Method

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 30

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

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

Factors of 820

List of positive integer factors of 820 that divides 820 without a remainder.

1,2,4,5,10,20,41,82,164,205,410,820

Greatest Common Factor

We found the factors 78,30,820 . The biggest common factor number is the GCF number.
So the greatest common factor 78,30,820 is 2.


LCM of Fractions Calculation Examples

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LCM of Fractions Calculation Examples

Frequently Asked Questions on Fractional LCM of 42/78, 27/30, 21/820

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 42/78, 27/30, 21/820?

Answer: LCM of Numerators as per given numbers 42/78, 27/30, 21/820 is

LCM of Numerators i.e. for 42,27,21 is 378

GCF of denominators i.e. for 78,30,820 is 2.

Thus, LCM of Fractions is 189.Finally, LCM of Fractions for 42/78, 27/30, 21/820 is 189.