Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 3/52, 8/39, 20/75, 52/343 quickly i.e. 1560 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 3/52, 8/39, 20/75, 52/343 is 1560.
LCM(3/52, 8/39, 20/75, 52/343) = 1560
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 3/52,8/39,20/75,52/343
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 3,8,20,52
Least Common Multiple of Numerators i.e. LCM of 3,8,20,52 is 1560.
GCF of Denominators means GCF of 52,39,75,343 as per the given fractions.
GCF of 52,39,75,343 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 3,8,20,52
2 | 3, 8, 20, 52 |
2 | 3, 4, 10, 26 |
3, 2, 5, 13 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 2 x 5 x 13 = 1560
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 3,8,20,52 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(3,8,20,52) = 1
common factors(in case of two or more numbers have common factors) = 16
GCF(3,8,20,52) x common factors =1 x 16 = 16
LCM(3,8,20,52) = ( 3 × 8 × 20 × 52 ) / 16
LCM(3,8,20,52) = 24960 / 16
LCM(3,8,20,52) = 1560
Lets's calculate GCF of 52,39,75,343
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 1560/1
Therefore the LCM of Fractions 3/52,8/39,20/75,52/343 is 1560
Factors of 52
List of positive integer factors of 52 that divides 52 without a remainder.
1,2,4,13,26,52
Factors of 39
List of positive integer factors of 39 that divides 39 without a remainder.
1,3,13,39
Factors of 75
List of positive integer factors of 75 that divides 75 without a remainder.
1,3,5,15,25,75
Factors of 343
List of positive integer factors of 343 that divides 343 without a remainder.
1,7,49,343
Greatest Common Factor
We found the factors 52,39,75,343 . The biggest common factor number is the GCF number.
So the greatest common factor 52,39,75,343 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 3/52, 8/39, 20/75, 52/343?
Answer: LCM of Numerators as per given numbers 3/52, 8/39, 20/75, 52/343 is
LCM of Numerators i.e. for 3,8,20,52 is 1560
GCF of denominators i.e. for 52,39,75,343 is 1.
Thus, LCM of Fractions is 1560.Finally, LCM of Fractions for 3/52, 8/39, 20/75, 52/343 is 1560.