Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 12/81, 21/82, 74/30, 84/529 quickly i.e. 3108 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 12/81, 21/82, 74/30, 84/529 is 3108.
LCM(12/81, 21/82, 74/30, 84/529) = 3108
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 12/81,21/82,74/30,84/529
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 12,21,74,84
Least Common Multiple of Numerators i.e. LCM of 12,21,74,84 is 3108.
GCF of Denominators means GCF of 81,82,30,529 as per the given fractions.
GCF of 81,82,30,529 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 12,21,74,84
2 | 12, 21, 74, 84 |
2 | 6, 21, 37, 42 |
3 | 3, 21, 37, 21 |
7 | 1, 7, 37, 7 |
1, 1, 37, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 7 x 1 x 1 x 37 x 1 = 3108
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 12,21,74,84 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(12,21,74,84) = 1
common factors(in case of two or more numbers have common factors) = 504
GCF(12,21,74,84) x common factors =1 x 504 = 504
LCM(12,21,74,84) = ( 12 × 21 × 74 × 84 ) / 504
LCM(12,21,74,84) = 1566432 / 504
LCM(12,21,74,84) = 3108
Lets's calculate GCF of 81,82,30,529
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 3108/1
Therefore the LCM of Fractions 12/81,21/82,74/30,84/529 is 3108
Factors of 81
List of positive integer factors of 81 that divides 81 without a remainder.
1,3,9,27,81
Factors of 82
List of positive integer factors of 82 that divides 82 without a remainder.
1,2,41,82
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 529
List of positive integer factors of 529 that divides 529 without a remainder.
1,23,529
Greatest Common Factor
We found the factors 81,82,30,529 . The biggest common factor number is the GCF number.
So the greatest common factor 81,82,30,529 is 1.
Here are some samples of LCM of Fractions calculations.
Here are some samples of LCM of Fractions calculations.
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 12/81, 21/82, 74/30, 84/529?
Answer: LCM of Numerators as per given numbers 12/81, 21/82, 74/30, 84/529 is
LCM of Numerators i.e. for 12,21,74,84 is 3108
GCF of denominators i.e. for 81,82,30,529 is 1.
Thus, LCM of Fractions is 3108.Finally, LCM of Fractions for 12/81, 21/82, 74/30, 84/529 is 3108.