Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 75/516, 20/518, 900/716 quickly i.e. 450 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 75/516, 20/518, 900/716 is 450.
LCM(75/516, 20/518, 900/716) = 450
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 75/516,20/518,900/716
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 75,20,900
Least Common Multiple of Numerators i.e. LCM of 75,20,900 is 900.
GCF of Denominators means GCF of 516,518,716 as per the given fractions.
GCF of 516,518,716 is 2 as it is the largest common factor for these numbers.
Lets's calculate LCM of 75,20,900
2 | 75, 20, 900 |
2 | 75, 10, 450 |
3 | 75, 5, 225 |
5 | 25, 5, 75 |
5 | 1, 5, 15 |
1, 1, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 5 x 1 x 1 x 3 = 900
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 75,20,900 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,20,900) = 5
common factors(in case of two or more numbers have common factors) = 300
GCF(75,20,900) x common factors =5 x 300 = 1500
LCM(75,20,900) = ( 75 × 20 × 900 ) / 1500
LCM(75,20,900) = 1350000 / 1500
LCM(75,20,900) = 900
Lets's calculate GCF of 516,518,716
2 | 516, 518, 716 |
258, 259, 358 |
∴ So the GCF of the given numbers is 2 = 2
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 900/2
Therefore the LCM of Fractions 75/516,20/518,900/716 is 450
Factors of 516
List of positive integer factors of 516 that divides 516 without a remainder.
1,2,3,4,6,12,43,86,129,172,258,516
Factors of 518
List of positive integer factors of 518 that divides 518 without a remainder.
1,2,7,14,37,74,259,518
Factors of 716
List of positive integer factors of 716 that divides 716 without a remainder.
1,2,4,179,358,716
Greatest Common Factor
We found the factors 516,518,716 . The biggest common factor number is the GCF number.
So the greatest common factor 516,518,716 is 2.
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 75/516, 20/518, 900/716?
Answer: LCM of Numerators as per given numbers 75/516, 20/518, 900/716 is
LCM of Numerators i.e. for 75,20,900 is 900
GCF of denominators i.e. for 516,518,716 is 2.
Thus, LCM of Fractions is 450.Finally, LCM of Fractions for 75/516, 20/518, 900/716 is 450.