Least Common Multiple of 12/68, 31/67, 71/70, 10/21

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Know Least Common Multiple of fractions 12/68, 31/67, 71/70, 10/21 quickly i.e. 132060 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.

Least Common Multiple (LCM) of 12/68, 31/67, 71/70, 10/21 is 132060.

LCM(12/68, 31/67, 71/70, 10/21) = 132060

LCM of 12/68, 31/67, 71/70, 10/21

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 12/68,31/67,71/70,10/21

Given numbers are 12/68,31/67,71/70,10/21

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 12,31,71,10

Least Common Multiple of Numerators i.e. LCM of 12,31,71,10 is 132060.

GCF of Denominators means GCF of 68,67,70,21 as per the given fractions.

GCF of 68,67,70,21 is 1 as it is the largest common factor for these numbers.

Lets's calculate LCM of 12,31,71,10

LCM of Fractions 12/68,31/67,71/70,10/21 is 132060

2 12, 31, 71, 10
6, 31, 71, 5

∴ So the LCM of the given numbers is 2 x 6 x 31 x 71 x 5 = 132060

Least Common Multiple of 12,31,71,10 with GCF Formula

Least Common Multiple of 12,31,71,10 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 12,31,71,10 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(12,31,71,10) = 1

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

GCF(12,31,71,10) x common factors =1 x 2 = 2

LCM(12,31,71,10) = ( 12 × 31 × 71 × 10 ) / 2

LCM(12,31,71,10) = 264120 / 2

LCM(12,31,71,10) = 132060


Lets's calculate GCF of 68,67,70,21

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

Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 132060/1

Therefore the LCM of Fractions 12/68,31/67,71/70,10/21 is 132060

Greatest Common Factor of 68,67,70,21 By Matching Biggest Common Factor Method

Greatest Common Factor of 68,67,70,21 By Matching Biggest Common Factor Method

Factors of 68

List of positive integer factors of 68 that divides 68 without a remainder.

1,2,4,17,34,68

Factors of 67

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

1,67

Factors of 70

List of positive integer factors of 70 that divides 70 without a remainder.

1,2,5,7,10,14,35,70

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 68,67,70,21 . The biggest common factor number is the GCF number.
So the greatest common factor 68,67,70,21 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 12/68, 31/67, 71/70, 10/21

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 12/68, 31/67, 71/70, 10/21?

Answer: LCM of Numerators as per given numbers 12/68, 31/67, 71/70, 10/21 is

LCM of Numerators i.e. for 12,31,71,10 is 132060

GCF of denominators i.e. for 68,67,70,21 is 1.

Thus, LCM of Fractions is 132060.Finally, LCM of Fractions for 12/68, 31/67, 71/70, 10/21 is 132060.