Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 57/74, 42/65, 48/108 quickly i.e. 6384 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 57/74, 42/65, 48/108 is 6384.
LCM(57/74, 42/65, 48/108) = 6384
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 57/74,42/65,48/108
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 57,42,48
Least Common Multiple of Numerators i.e. LCM of 57,42,48 is 6384.
GCF of Denominators means GCF of 74,65,108 as per the given fractions.
GCF of 74,65,108 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 57,42,48
2 | 57, 42, 48 |
3 | 57, 21, 24 |
19, 7, 8 |
∴ So the LCM of the given numbers is 2 x 3 x 19 x 7 x 8 = 6384
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 57,42,48 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(57,42,48) = 3
common factors(in case of two or more numbers have common factors) = 6
GCF(57,42,48) x common factors =3 x 6 = 18
LCM(57,42,48) = ( 57 × 42 × 48 ) / 18
LCM(57,42,48) = 114912 / 18
LCM(57,42,48) = 6384
Lets's calculate GCF of 74,65,108
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 6384/1
Therefore the LCM of Fractions 57/74,42/65,48/108 is 6384
Factors of 74
List of positive integer factors of 74 that divides 74 without a remainder.
1,2,37,74
Factors of 65
List of positive integer factors of 65 that divides 65 without a remainder.
1,5,13,65
Factors of 108
List of positive integer factors of 108 that divides 108 without a remainder.
1,2,3,4,6,9,12,18,27,36,54,108
Greatest Common Factor
We found the factors 74,65,108 . The biggest common factor number is the GCF number.
So the greatest common factor 74,65,108 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 57/74, 42/65, 48/108?
Answer: LCM of Numerators as per given numbers 57/74, 42/65, 48/108 is
LCM of Numerators i.e. for 57,42,48 is 6384
GCF of denominators i.e. for 74,65,108 is 1.
Thus, LCM of Fractions is 6384.Finally, LCM of Fractions for 57/74, 42/65, 48/108 is 6384.