Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 20/68, 720/14, 378/254 quickly i.e. 7560 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 20/68, 720/14, 378/254 is 7560.
LCM(20/68, 720/14, 378/254) = 7560
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 20/68,720/14,378/254
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 20,720,378
Least Common Multiple of Numerators i.e. LCM of 20,720,378 is 15120.
GCF of Denominators means GCF of 68,14,254 as per the given fractions.
GCF of 68,14,254 is 2 as it is the largest common factor for these numbers.
Lets's calculate LCM of 20,720,378
2 | 20, 720, 378 |
2 | 10, 360, 189 |
3 | 5, 180, 189 |
3 | 5, 60, 63 |
5 | 5, 20, 21 |
1, 4, 21 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 5 x 1 x 4 x 21 = 15120
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 20,720,378 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(20,720,378) = 2
common factors(in case of two or more numbers have common factors) = 180
GCF(20,720,378) x common factors =2 x 180 = 360
LCM(20,720,378) = ( 20 × 720 × 378 ) / 360
LCM(20,720,378) = 5443200 / 360
LCM(20,720,378) = 15120
Lets's calculate GCF of 68,14,254
2 | 68, 14, 254 |
34, 7, 127 |
∴ So the GCF of the given numbers is 2 = 2
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 15120/2
Therefore the LCM of Fractions 20/68,720/14,378/254 is 7560
Factors of 68
List of positive integer factors of 68 that divides 68 without a remainder.
1,2,4,17,34,68
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1,2,7,14
Factors of 254
List of positive integer factors of 254 that divides 254 without a remainder.
1,2,127,254
Greatest Common Factor
We found the factors 68,14,254 . The biggest common factor number is the GCF number.
So the greatest common factor 68,14,254 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 20/68, 720/14, 378/254?
Answer: LCM of Numerators as per given numbers 20/68, 720/14, 378/254 is
LCM of Numerators i.e. for 20,720,378 is 15120
GCF of denominators i.e. for 68,14,254 is 2.
Thus, LCM of Fractions is 7560.Finally, LCM of Fractions for 20/68, 720/14, 378/254 is 7560.