Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 270/75, 213/81, 512/426 quickly i.e. 1635840 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 270/75, 213/81, 512/426 is 1635840.
LCM(270/75, 213/81, 512/426) = 1635840
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 270/75,213/81,512/426
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 270,213,512
Least Common Multiple of Numerators i.e. LCM of 270,213,512 is 4907520.
GCF of Denominators means GCF of 75,81,426 as per the given fractions.
GCF of 75,81,426 is 3 as it is the largest common factor for these numbers.
Lets's calculate LCM of 270,213,512
2 | 270, 213, 512 |
3 | 135, 213, 256 |
45, 71, 256 |
∴ So the LCM of the given numbers is 2 x 3 x 45 x 71 x 256 = 4907520
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 270,213,512 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(270,213,512) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(270,213,512) x common factors =1 x 6 = 6
LCM(270,213,512) = ( 270 × 213 × 512 ) / 6
LCM(270,213,512) = 29445120 / 6
LCM(270,213,512) = 4907520
Lets's calculate GCF of 75,81,426
3 | 75, 81, 426 |
25, 27, 142 |
∴ So the GCF of the given numbers is 3 = 3
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 4907520/3
Therefore the LCM of Fractions 270/75,213/81,512/426 is 1635840
Factors of 75
List of positive integer factors of 75 that divides 75 without a remainder.
1,3,5,15,25,75
Factors of 81
List of positive integer factors of 81 that divides 81 without a remainder.
1,3,9,27,81
Factors of 426
List of positive integer factors of 426 that divides 426 without a remainder.
1,2,3,6,71,142,213,426
Greatest Common Factor
We found the factors 75,81,426 . The biggest common factor number is the GCF number.
So the greatest common factor 75,81,426 is 3.
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 270/75, 213/81, 512/426?
Answer: LCM of Numerators as per given numbers 270/75, 213/81, 512/426 is
LCM of Numerators i.e. for 270,213,512 is 4907520
GCF of denominators i.e. for 75,81,426 is 3.
Thus, LCM of Fractions is 1635840.Finally, LCM of Fractions for 270/75, 213/81, 512/426 is 1635840.