Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 5/60, 70/82, 88/84, 20/68 quickly i.e. 1540 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 5/60, 70/82, 88/84, 20/68 is 1540.
LCM(5/60, 70/82, 88/84, 20/68) = 1540
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 5/60,70/82,88/84,20/68
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 5,70,88,20
Least Common Multiple of Numerators i.e. LCM of 5,70,88,20 is 3080.
GCF of Denominators means GCF of 60,82,84,68 as per the given fractions.
GCF of 60,82,84,68 is 2 as it is the largest common factor for these numbers.
Lets's calculate LCM of 5,70,88,20
2 | 5, 70, 88, 20 |
2 | 5, 35, 44, 10 |
5 | 5, 35, 22, 5 |
1, 7, 22, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 1 x 7 x 22 x 1 = 3080
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 5,70,88,20 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(5,70,88,20) = 1
common factors(in case of two or more numbers have common factors) = 200
GCF(5,70,88,20) x common factors =1 x 200 = 200
LCM(5,70,88,20) = ( 5 × 70 × 88 × 20 ) / 200
LCM(5,70,88,20) = 616000 / 200
LCM(5,70,88,20) = 3080
Lets's calculate GCF of 60,82,84,68
2 | 60, 82, 84, 68 |
30, 41, 42, 34 |
∴ So the GCF of the given numbers is 2 = 2
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 3080/2
Therefore the LCM of Fractions 5/60,70/82,88/84,20/68 is 1540
Factors of 60
List of positive integer factors of 60 that divides 60 without a remainder.
1,2,3,4,5,6,10,12,15,20,30,60
Factors of 82
List of positive integer factors of 82 that divides 82 without a remainder.
1,2,41,82
Factors of 84
List of positive integer factors of 84 that divides 84 without a remainder.
1,2,3,4,6,7,12,14,21,28,42,84
Factors of 68
List of positive integer factors of 68 that divides 68 without a remainder.
1,2,4,17,34,68
Greatest Common Factor
We found the factors 60,82,84,68 . The biggest common factor number is the GCF number.
So the greatest common factor 60,82,84,68 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 5/60, 70/82, 88/84, 20/68?
Answer: LCM of Numerators as per given numbers 5/60, 70/82, 88/84, 20/68 is
LCM of Numerators i.e. for 5,70,88,20 is 3080
GCF of denominators i.e. for 60,82,84,68 is 2.
Thus, LCM of Fractions is 1540.Finally, LCM of Fractions for 5/60, 70/82, 88/84, 20/68 is 1540.