Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 78/82, 26/44, 17/14, 42/136 quickly i.e. 4641 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 78/82, 26/44, 17/14, 42/136 is 4641.
LCM(78/82, 26/44, 17/14, 42/136) = 4641
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 78/82,26/44,17/14,42/136
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 78,26,17,42
Least Common Multiple of Numerators i.e. LCM of 78,26,17,42 is 9282.
GCF of Denominators means GCF of 82,44,14,136 as per the given fractions.
GCF of 82,44,14,136 is 2 as it is the largest common factor for these numbers.
Lets's calculate LCM of 78,26,17,42
2 | 78, 26, 17, 42 |
3 | 39, 13, 17, 21 |
13 | 13, 13, 17, 7 |
1, 1, 17, 7 |
∴ So the LCM of the given numbers is 2 x 3 x 13 x 1 x 1 x 17 x 7 = 9282
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 78,26,17,42 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,26,17,42) = 1
common factors(in case of two or more numbers have common factors) = 156
GCF(78,26,17,42) x common factors =1 x 156 = 156
LCM(78,26,17,42) = ( 78 × 26 × 17 × 42 ) / 156
LCM(78,26,17,42) = 1447992 / 156
LCM(78,26,17,42) = 9282
Lets's calculate GCF of 82,44,14,136
2 | 82, 44, 14, 136 |
41, 22, 7, 68 |
∴ So the GCF of the given numbers is 2 = 2
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 9282/2
Therefore the LCM of Fractions 78/82,26/44,17/14,42/136 is 4641
Factors of 82
List of positive integer factors of 82 that divides 82 without a remainder.
1,2,41,82
Factors of 44
List of positive integer factors of 44 that divides 44 without a remainder.
1,2,4,11,22,44
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1,2,7,14
Factors of 136
List of positive integer factors of 136 that divides 136 without a remainder.
1,2,4,8,17,34,68,136
Greatest Common Factor
We found the factors 82,44,14,136 . The biggest common factor number is the GCF number.
So the greatest common factor 82,44,14,136 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 78/82, 26/44, 17/14, 42/136?
Answer: LCM of Numerators as per given numbers 78/82, 26/44, 17/14, 42/136 is
LCM of Numerators i.e. for 78,26,17,42 is 9282
GCF of denominators i.e. for 82,44,14,136 is 2.
Thus, LCM of Fractions is 4641.Finally, LCM of Fractions for 78/82, 26/44, 17/14, 42/136 is 4641.