Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 34/14, 85/43, 18/61, 40/989 quickly i.e. 6120 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 34/14, 85/43, 18/61, 40/989 is 6120.
LCM(34/14, 85/43, 18/61, 40/989) = 6120
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 34/14,85/43,18/61,40/989
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 34,85,18,40
Least Common Multiple of Numerators i.e. LCM of 34,85,18,40 is 6120.
GCF of Denominators means GCF of 14,43,61,989 as per the given fractions.
GCF of 14,43,61,989 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 34,85,18,40
2 | 34, 85, 18, 40 |
5 | 17, 85, 9, 20 |
17 | 17, 17, 9, 4 |
1, 1, 9, 4 |
∴ So the LCM of the given numbers is 2 x 5 x 17 x 1 x 1 x 9 x 4 = 6120
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 34,85,18,40 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,85,18,40) = 1
common factors(in case of two or more numbers have common factors) = 340
GCF(34,85,18,40) x common factors =1 x 340 = 340
LCM(34,85,18,40) = ( 34 × 85 × 18 × 40 ) / 340
LCM(34,85,18,40) = 2080800 / 340
LCM(34,85,18,40) = 6120
Lets's calculate GCF of 14,43,61,989
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 6120/1
Therefore the LCM of Fractions 34/14,85/43,18/61,40/989 is 6120
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1,2,7,14
Factors of 43
List of positive integer factors of 43 that divides 43 without a remainder.
1,43
Factors of 61
List of positive integer factors of 61 that divides 61 without a remainder.
1,61
Factors of 989
List of positive integer factors of 989 that divides 989 without a remainder.
1,23,43,989
Greatest Common Factor
We found the factors 14,43,61,989 . The biggest common factor number is the GCF number.
So the greatest common factor 14,43,61,989 is 1.
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 34/14, 85/43, 18/61, 40/989?
Answer: LCM of Numerators as per given numbers 34/14, 85/43, 18/61, 40/989 is
LCM of Numerators i.e. for 34,85,18,40 is 6120
GCF of denominators i.e. for 14,43,61,989 is 1.
Thus, LCM of Fractions is 6120.Finally, LCM of Fractions for 34/14, 85/43, 18/61, 40/989 is 6120.