Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 31/120, 80/824, 788/260 quickly i.e. 122140 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 31/120, 80/824, 788/260 is 122140.
LCM(31/120, 80/824, 788/260) = 122140
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 31/120,80/824,788/260
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 31,80,788
Least Common Multiple of Numerators i.e. LCM of 31,80,788 is 488560.
GCF of Denominators means GCF of 120,824,260 as per the given fractions.
GCF of 120,824,260 is 4 as it is the largest common factor for these numbers.
Lets's calculate LCM of 31,80,788
2 | 31, 80, 788 |
2 | 31, 40, 394 |
31, 20, 197 |
∴ So the LCM of the given numbers is 2 x 2 x 31 x 20 x 197 = 488560
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 31,80,788 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,80,788) = 1
common factors(in case of two or more numbers have common factors) = 4
GCF(31,80,788) x common factors =1 x 4 = 4
LCM(31,80,788) = ( 31 × 80 × 788 ) / 4
LCM(31,80,788) = 1954240 / 4
LCM(31,80,788) = 488560
Lets's calculate GCF of 120,824,260
2 | 120, 824, 260 |
2 | 60, 412, 130 |
30, 206, 65 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 488560/4
Therefore the LCM of Fractions 31/120,80/824,788/260 is 122140
Factors of 120
List of positive integer factors of 120 that divides 120 without a remainder.
1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
Factors of 824
List of positive integer factors of 824 that divides 824 without a remainder.
1,2,4,8,103,206,412,824
Factors of 260
List of positive integer factors of 260 that divides 260 without a remainder.
1,2,4,5,10,13,20,26,52,65,130,260
Greatest Common Factor
We found the factors 120,824,260 . The biggest common factor number is the GCF number.
So the greatest common factor 120,824,260 is 4.
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 31/120, 80/824, 788/260?
Answer: LCM of Numerators as per given numbers 31/120, 80/824, 788/260 is
LCM of Numerators i.e. for 31,80,788 is 488560
GCF of denominators i.e. for 120,824,260 is 4.
Thus, LCM of Fractions is 122140.Finally, LCM of Fractions for 31/120, 80/824, 788/260 is 122140.