Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 20/70, 31/68, 60/40, 75/933 quickly i.e. 9300 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 20/70, 31/68, 60/40, 75/933 is 9300.
LCM(20/70, 31/68, 60/40, 75/933) = 9300
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 20/70,31/68,60/40,75/933
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 20,31,60,75
Least Common Multiple of Numerators i.e. LCM of 20,31,60,75 is 9300.
GCF of Denominators means GCF of 70,68,40,933 as per the given fractions.
GCF of 70,68,40,933 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 20,31,60,75
2 | 20, 31, 60, 75 |
2 | 10, 31, 30, 75 |
3 | 5, 31, 15, 75 |
5 | 5, 31, 5, 25 |
1, 31, 1, 5 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 1 x 31 x 1 x 5 = 9300
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 20,31,60,75 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(20,31,60,75) = 1
common factors(in case of two or more numbers have common factors) = 300
GCF(20,31,60,75) x common factors =1 x 300 = 300
LCM(20,31,60,75) = ( 20 × 31 × 60 × 75 ) / 300
LCM(20,31,60,75) = 2790000 / 300
LCM(20,31,60,75) = 9300
Lets's calculate GCF of 70,68,40,933
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 9300/1
Therefore the LCM of Fractions 20/70,31/68,60/40,75/933 is 9300
Factors of 70
List of positive integer factors of 70 that divides 70 without a remainder.
1,2,5,7,10,14,35,70
Factors of 68
List of positive integer factors of 68 that divides 68 without a remainder.
1,2,4,17,34,68
Factors of 40
List of positive integer factors of 40 that divides 40 without a remainder.
1,2,4,5,8,10,20,40
Factors of 933
List of positive integer factors of 933 that divides 933 without a remainder.
1,3,311,933
Greatest Common Factor
We found the factors 70,68,40,933 . The biggest common factor number is the GCF number.
So the greatest common factor 70,68,40,933 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 20/70, 31/68, 60/40, 75/933?
Answer: LCM of Numerators as per given numbers 20/70, 31/68, 60/40, 75/933 is
LCM of Numerators i.e. for 20,31,60,75 is 9300
GCF of denominators i.e. for 70,68,40,933 is 1.
Thus, LCM of Fractions is 9300.Finally, LCM of Fractions for 20/70, 31/68, 60/40, 75/933 is 9300.