Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 30/45, 30/71, 85/85, 507/31 quickly i.e. 86190 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 30/45, 30/71, 85/85, 507/31 is 86190.
LCM(30/45, 30/71, 85/85, 507/31) = 86190
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 30/45,30/71,85/85,507/31
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 30,30,85,507
Least Common Multiple of Numerators i.e. LCM of 30,30,85,507 is 86190.
GCF of Denominators means GCF of 45,71,85,31 as per the given fractions.
GCF of 45,71,85,31 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 30,30,85,507
2 | 30, 30, 85, 507 |
3 | 15, 15, 85, 507 |
5 | 5, 5, 85, 169 |
1, 1, 17, 169 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 1 x 1 x 17 x 169 = 86190
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 30,30,85,507 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,30,85,507) = 1
common factors(in case of two or more numbers have common factors) = 450
GCF(30,30,85,507) x common factors =1 x 450 = 450
LCM(30,30,85,507) = ( 30 × 30 × 85 × 507 ) / 450
LCM(30,30,85,507) = 38785500 / 450
LCM(30,30,85,507) = 86190
Lets's calculate GCF of 45,71,85,31
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 86190/1
Therefore the LCM of Fractions 30/45,30/71,85/85,507/31 is 86190
Factors of 45
List of positive integer factors of 45 that divides 45 without a remainder.
1,3,5,9,15,45
Factors of 71
List of positive integer factors of 71 that divides 71 without a remainder.
1,71
Factors of 85
List of positive integer factors of 85 that divides 85 without a remainder.
1,5,17,85
Factors of 31
List of positive integer factors of 31 that divides 31 without a remainder.
1,31
Greatest Common Factor
We found the factors 45,71,85,31 . The biggest common factor number is the GCF number.
So the greatest common factor 45,71,85,31 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 30/45, 30/71, 85/85, 507/31?
Answer: LCM of Numerators as per given numbers 30/45, 30/71, 85/85, 507/31 is
LCM of Numerators i.e. for 30,30,85,507 is 86190
GCF of denominators i.e. for 45,71,85,31 is 1.
Thus, LCM of Fractions is 86190.Finally, LCM of Fractions for 30/45, 30/71, 85/85, 507/31 is 86190.