Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 31/68, 24/78, 49/13, 80/116 quickly i.e. 364560 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 31/68, 24/78, 49/13, 80/116 is 364560.
LCM(31/68, 24/78, 49/13, 80/116) = 364560
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 31/68,24/78,49/13,80/116
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 31,24,49,80
Least Common Multiple of Numerators i.e. LCM of 31,24,49,80 is 364560.
GCF of Denominators means GCF of 68,78,13,116 as per the given fractions.
GCF of 68,78,13,116 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 31,24,49,80
2 | 31, 24, 49, 80 |
2 | 31, 12, 49, 40 |
2 | 31, 6, 49, 20 |
31, 3, 49, 10 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 31 x 3 x 49 x 10 = 364560
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 31,24,49,80 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,24,49,80) = 1
common factors(in case of two or more numbers have common factors) = 8
GCF(31,24,49,80) x common factors =1 x 8 = 8
LCM(31,24,49,80) = ( 31 × 24 × 49 × 80 ) / 8
LCM(31,24,49,80) = 2916480 / 8
LCM(31,24,49,80) = 364560
Lets's calculate GCF of 68,78,13,116
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 364560/1
Therefore the LCM of Fractions 31/68,24/78,49/13,80/116 is 364560
Factors of 68
List of positive integer factors of 68 that divides 68 without a remainder.
1,2,4,17,34,68
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 13
List of positive integer factors of 13 that divides 13 without a remainder.
1,13
Factors of 116
List of positive integer factors of 116 that divides 116 without a remainder.
1,2,4,29,58,116
Greatest Common Factor
We found the factors 68,78,13,116 . The biggest common factor number is the GCF number.
So the greatest common factor 68,78,13,116 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 31/68, 24/78, 49/13, 80/116?
Answer: LCM of Numerators as per given numbers 31/68, 24/78, 49/13, 80/116 is
LCM of Numerators i.e. for 31,24,49,80 is 364560
GCF of denominators i.e. for 68,78,13,116 is 1.
Thus, LCM of Fractions is 364560.Finally, LCM of Fractions for 31/68, 24/78, 49/13, 80/116 is 364560.