Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 39/30, 61/12, 823/612 quickly i.e. 1957917/6 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 39/30, 61/12, 823/612 is 1957917/6.
LCM(39/30, 61/12, 823/612) = 1957917/6
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 39/30,61/12,823/612
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 39,61,823
Least Common Multiple of Numerators i.e. LCM of 39,61,823 is 1957917.
GCF of Denominators means GCF of 30,12,612 as per the given fractions.
GCF of 30,12,612 is 6 as it is the largest common factor for these numbers.
Lets's calculate LCM of 39,61,823
Given numbers has no common factors except 1. So, there LCM is their product i.e 1957917
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 39,61,823 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(39,61,823) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(39,61,823) x common factors =1 x 1 = 1
LCM(39,61,823) = ( 39 × 61 × 823 ) / 1
LCM(39,61,823) = 1957917 / 1
LCM(39,61,823) = 1957917
Lets's calculate GCF of 30,12,612
2 | 30, 12, 612 |
3 | 15, 6, 306 |
5, 2, 102 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 1957917/6
Therefore the LCM of Fractions 39/30,61/12,823/612 is 1957917/6
Factors of 30
List of positive integer factors of 30 that divides 30 without a remainder.
1,2,3,5,6,10,15,30
Factors of 12
List of positive integer factors of 12 that divides 12 without a remainder.
1,2,3,4,6,12
Factors of 612
List of positive integer factors of 612 that divides 612 without a remainder.
1,2,3,4,6,9,12,17,18,34,36,51,68,102,153,204,306,612
Greatest Common Factor
We found the factors 30,12,612 . The biggest common factor number is the GCF number.
So the greatest common factor 30,12,612 is 6.
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 39/30, 61/12, 823/612?
Answer: LCM of Numerators as per given numbers 39/30, 61/12, 823/612 is
LCM of Numerators i.e. for 39,61,823 is 1957917
GCF of denominators i.e. for 30,12,612 is 6.
Thus, LCM of Fractions is 1957917/6.Finally, LCM of Fractions for 39/30, 61/12, 823/612 is 1957917/6.