Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 30/36, 30/24, 85/82, 56/725 quickly i.e. 14280 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 30/36, 30/24, 85/82, 56/725 is 14280.
LCM(30/36, 30/24, 85/82, 56/725) = 14280
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 30/36,30/24,85/82,56/725
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 30,30,85,56
Least Common Multiple of Numerators i.e. LCM of 30,30,85,56 is 14280.
GCF of Denominators means GCF of 36,24,82,725 as per the given fractions.
GCF of 36,24,82,725 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 30,30,85,56
2 | 30, 30, 85, 56 |
3 | 15, 15, 85, 28 |
5 | 5, 5, 85, 28 |
1, 1, 17, 28 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 1 x 1 x 17 x 28 = 14280
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 30,30,85,56 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,30,85,56) = 1
common factors(in case of two or more numbers have common factors) = 300
GCF(30,30,85,56) x common factors =1 x 300 = 300
LCM(30,30,85,56) = ( 30 × 30 × 85 × 56 ) / 300
LCM(30,30,85,56) = 4284000 / 300
LCM(30,30,85,56) = 14280
Lets's calculate GCF of 36,24,82,725
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 14280/1
Therefore the LCM of Fractions 30/36,30/24,85/82,56/725 is 14280
Factors of 36
List of positive integer factors of 36 that divides 36 without a remainder.
1,2,3,4,6,9,12,18,36
Factors of 24
List of positive integer factors of 24 that divides 24 without a remainder.
1,2,3,4,6,8,12,24
Factors of 82
List of positive integer factors of 82 that divides 82 without a remainder.
1,2,41,82
Factors of 725
List of positive integer factors of 725 that divides 725 without a remainder.
1,5,25,29,145,725
Greatest Common Factor
We found the factors 36,24,82,725 . The biggest common factor number is the GCF number.
So the greatest common factor 36,24,82,725 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 30/36, 30/24, 85/82, 56/725?
Answer: LCM of Numerators as per given numbers 30/36, 30/24, 85/82, 56/725 is
LCM of Numerators i.e. for 30,30,85,56 is 14280
GCF of denominators i.e. for 36,24,82,725 is 1.
Thus, LCM of Fractions is 14280.Finally, LCM of Fractions for 30/36, 30/24, 85/82, 56/725 is 14280.