Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 57/14, 68/390, 240/755 quickly i.e. 77520 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 57/14, 68/390, 240/755 is 77520.
LCM(57/14, 68/390, 240/755) = 77520
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 57/14,68/390,240/755
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 57,68,240
Least Common Multiple of Numerators i.e. LCM of 57,68,240 is 77520.
GCF of Denominators means GCF of 14,390,755 as per the given fractions.
GCF of 14,390,755 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 57,68,240
2 | 57, 68, 240 |
2 | 57, 34, 120 |
3 | 57, 17, 60 |
19, 17, 20 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 19 x 17 x 20 = 77520
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 57,68,240 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(57,68,240) = 1
common factors(in case of two or more numbers have common factors) = 12
GCF(57,68,240) x common factors =1 x 12 = 12
LCM(57,68,240) = ( 57 × 68 × 240 ) / 12
LCM(57,68,240) = 930240 / 12
LCM(57,68,240) = 77520
Lets's calculate GCF of 14,390,755
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 77520/1
Therefore the LCM of Fractions 57/14,68/390,240/755 is 77520
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1,2,7,14
Factors of 390
List of positive integer factors of 390 that divides 390 without a remainder.
1,2,3,5,6,10,13,15,26,30,39,65,78,130,195,390
Factors of 755
List of positive integer factors of 755 that divides 755 without a remainder.
1,5,151,755
Greatest Common Factor
We found the factors 14,390,755 . The biggest common factor number is the GCF number.
So the greatest common factor 14,390,755 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 57/14, 68/390, 240/755?
Answer: LCM of Numerators as per given numbers 57/14, 68/390, 240/755 is
LCM of Numerators i.e. for 57,68,240 is 77520
GCF of denominators i.e. for 14,390,755 is 1.
Thus, LCM of Fractions is 77520.Finally, LCM of Fractions for 57/14, 68/390, 240/755 is 77520.