Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 30/678, 20/558, 117/746 quickly i.e. 1170 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 30/678, 20/558, 117/746 is 1170.
LCM(30/678, 20/558, 117/746) = 1170
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 30/678,20/558,117/746
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 30,20,117
Least Common Multiple of Numerators i.e. LCM of 30,20,117 is 2340.
GCF of Denominators means GCF of 678,558,746 as per the given fractions.
GCF of 678,558,746 is 2 as it is the largest common factor for these numbers.
Lets's calculate LCM of 30,20,117
2 | 30, 20, 117 |
3 | 15, 10, 117 |
5 | 5, 10, 39 |
1, 2, 39 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 1 x 2 x 39 = 2340
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 30,20,117 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,20,117) = 1
common factors(in case of two or more numbers have common factors) = 30
GCF(30,20,117) x common factors =1 x 30 = 30
LCM(30,20,117) = ( 30 × 20 × 117 ) / 30
LCM(30,20,117) = 70200 / 30
LCM(30,20,117) = 2340
Lets's calculate GCF of 678,558,746
2 | 678, 558, 746 |
339, 279, 373 |
∴ So the GCF of the given numbers is 2 = 2
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 2340/2
Therefore the LCM of Fractions 30/678,20/558,117/746 is 1170
Factors of 678
List of positive integer factors of 678 that divides 678 without a remainder.
1,2,3,6,113,226,339,678
Factors of 558
List of positive integer factors of 558 that divides 558 without a remainder.
1,2,3,6,9,18,31,62,93,186,279,558
Factors of 746
List of positive integer factors of 746 that divides 746 without a remainder.
1,2,373,746
Greatest Common Factor
We found the factors 678,558,746 . The biggest common factor number is the GCF number.
So the greatest common factor 678,558,746 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 30/678, 20/558, 117/746?
Answer: LCM of Numerators as per given numbers 30/678, 20/558, 117/746 is
LCM of Numerators i.e. for 30,20,117 is 2340
GCF of denominators i.e. for 678,558,746 is 2.
Thus, LCM of Fractions is 1170.Finally, LCM of Fractions for 30/678, 20/558, 117/746 is 1170.