Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 810/18, 420/80, 285/416 quickly i.e. 107730 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 810/18, 420/80, 285/416 is 107730.
LCM(810/18, 420/80, 285/416) = 107730
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 810/18,420/80,285/416
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 810,420,285
Least Common Multiple of Numerators i.e. LCM of 810,420,285 is 215460.
GCF of Denominators means GCF of 18,80,416 as per the given fractions.
GCF of 18,80,416 is 2 as it is the largest common factor for these numbers.
Lets's calculate LCM of 810,420,285
2 | 810, 420, 285 |
3 | 405, 210, 285 |
5 | 135, 70, 95 |
27, 14, 19 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 27 x 14 x 19 = 215460
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 810,420,285 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(810,420,285) = 15
common factors(in case of two or more numbers have common factors) = 30
GCF(810,420,285) x common factors =15 x 30 = 450
LCM(810,420,285) = ( 810 × 420 × 285 ) / 450
LCM(810,420,285) = 96957000 / 450
LCM(810,420,285) = 215460
Lets's calculate GCF of 18,80,416
2 | 18, 80, 416 |
9, 40, 208 |
∴ So the GCF of the given numbers is 2 = 2
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 215460/2
Therefore the LCM of Fractions 810/18,420/80,285/416 is 107730
Factors of 18
List of positive integer factors of 18 that divides 18 without a remainder.
1,2,3,6,9,18
Factors of 80
List of positive integer factors of 80 that divides 80 without a remainder.
1,2,4,5,8,10,16,20,40,80
Factors of 416
List of positive integer factors of 416 that divides 416 without a remainder.
1,2,4,8,13,16,26,32,52,104,208,416
Greatest Common Factor
We found the factors 18,80,416 . The biggest common factor number is the GCF number.
So the greatest common factor 18,80,416 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 810/18, 420/80, 285/416?
Answer: LCM of Numerators as per given numbers 810/18, 420/80, 285/416 is
LCM of Numerators i.e. for 810,420,285 is 215460
GCF of denominators i.e. for 18,80,416 is 2.
Thus, LCM of Fractions is 107730.Finally, LCM of Fractions for 810/18, 420/80, 285/416 is 107730.