Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 82/67, 10/26, 91/49, 65/18 quickly i.e. 37310 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 82/67, 10/26, 91/49, 65/18 is 37310.
LCM(82/67, 10/26, 91/49, 65/18) = 37310
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 82/67,10/26,91/49,65/18
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 82,10,91,65
Least Common Multiple of Numerators i.e. LCM of 82,10,91,65 is 37310.
GCF of Denominators means GCF of 67,26,49,18 as per the given fractions.
GCF of 67,26,49,18 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 82,10,91,65
2 | 82, 10, 91, 65 |
5 | 41, 5, 91, 65 |
13 | 41, 1, 91, 13 |
41, 1, 7, 1 |
∴ So the LCM of the given numbers is 2 x 5 x 13 x 41 x 1 x 7 x 1 = 37310
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 82,10,91,65 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(82,10,91,65) = 1
common factors(in case of two or more numbers have common factors) = 130
GCF(82,10,91,65) x common factors =1 x 130 = 130
LCM(82,10,91,65) = ( 82 × 10 × 91 × 65 ) / 130
LCM(82,10,91,65) = 4850300 / 130
LCM(82,10,91,65) = 37310
Lets's calculate GCF of 67,26,49,18
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 37310/1
Therefore the LCM of Fractions 82/67,10/26,91/49,65/18 is 37310
Factors of 67
List of positive integer factors of 67 that divides 67 without a remainder.
1,67
Factors of 26
List of positive integer factors of 26 that divides 26 without a remainder.
1,2,13,26
Factors of 49
List of positive integer factors of 49 that divides 49 without a remainder.
1,7,49
Factors of 18
List of positive integer factors of 18 that divides 18 without a remainder.
1,2,3,6,9,18
Greatest Common Factor
We found the factors 67,26,49,18 . The biggest common factor number is the GCF number.
So the greatest common factor 67,26,49,18 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 82/67, 10/26, 91/49, 65/18?
Answer: LCM of Numerators as per given numbers 82/67, 10/26, 91/49, 65/18 is
LCM of Numerators i.e. for 82,10,91,65 is 37310
GCF of denominators i.e. for 67,26,49,18 is 1.
Thus, LCM of Fractions is 37310.Finally, LCM of Fractions for 82/67, 10/26, 91/49, 65/18 is 37310.