Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 31/40, 15/29, 90/60, 54/84 quickly i.e. 8370 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 31/40, 15/29, 90/60, 54/84 is 8370.
LCM(31/40, 15/29, 90/60, 54/84) = 8370
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 31/40,15/29,90/60,54/84
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 31,15,90,54
Least Common Multiple of Numerators i.e. LCM of 31,15,90,54 is 8370.
GCF of Denominators means GCF of 40,29,60,84 as per the given fractions.
GCF of 40,29,60,84 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 31,15,90,54
2 | 31, 15, 90, 54 |
3 | 31, 15, 45, 27 |
3 | 31, 5, 15, 9 |
5 | 31, 5, 5, 3 |
31, 1, 1, 3 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 5 x 31 x 1 x 1 x 3 = 8370
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 31,15,90,54 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,15,90,54) = 1
common factors(in case of two or more numbers have common factors) = 270
GCF(31,15,90,54) x common factors =1 x 270 = 270
LCM(31,15,90,54) = ( 31 × 15 × 90 × 54 ) / 270
LCM(31,15,90,54) = 2259900 / 270
LCM(31,15,90,54) = 8370
Lets's calculate GCF of 40,29,60,84
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 8370/1
Therefore the LCM of Fractions 31/40,15/29,90/60,54/84 is 8370
Factors of 40
List of positive integer factors of 40 that divides 40 without a remainder.
1,2,4,5,8,10,20,40
Factors of 29
List of positive integer factors of 29 that divides 29 without a remainder.
1,29
Factors of 60
List of positive integer factors of 60 that divides 60 without a remainder.
1,2,3,4,5,6,10,12,15,20,30,60
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 40,29,60,84 . The biggest common factor number is the GCF number.
So the greatest common factor 40,29,60,84 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 31/40, 15/29, 90/60, 54/84?
Answer: LCM of Numerators as per given numbers 31/40, 15/29, 90/60, 54/84 is
LCM of Numerators i.e. for 31,15,90,54 is 8370
GCF of denominators i.e. for 40,29,60,84 is 1.
Thus, LCM of Fractions is 8370.Finally, LCM of Fractions for 31/40, 15/29, 90/60, 54/84 is 8370.