Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 21/9, 56/75, 23/17 quickly i.e. 3864 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 21/9, 56/75, 23/17 is 3864.
LCM(21/9, 56/75, 23/17) = 3864
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 21/9,56/75,23/17
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 21,56,23
Least Common Multiple of Numerators i.e. LCM of 21,56,23 is 3864.
GCF of Denominators means GCF of 9,75,17 as per the given fractions.
GCF of 9,75,17 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 21,56,23
7 | 21, 56, 23 |
3, 8, 23 |
∴ So the LCM of the given numbers is 7 x 3 x 8 x 23 = 3864
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 21,56,23 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,56,23) = 1
common factors(in case of two or more numbers have common factors) = 7
GCF(21,56,23) x common factors =1 x 7 = 7
LCM(21,56,23) = ( 21 × 56 × 23 ) / 7
LCM(21,56,23) = 27048 / 7
LCM(21,56,23) = 3864
Lets's calculate GCF of 9,75,17
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 3864/1
Therefore the LCM of Fractions 21/9,56/75,23/17 is 3864
Factors of 9
List of positive integer factors of 9 that divides 9 without a remainder.
1,3,9
Factors of 75
List of positive integer factors of 75 that divides 75 without a remainder.
1,3,5,15,25,75
Factors of 17
List of positive integer factors of 17 that divides 17 without a remainder.
1,17
Greatest Common Factor
We found the factors 9,75,17 . The biggest common factor number is the GCF number.
So the greatest common factor 9,75,17 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 21/9, 56/75, 23/17?
Answer: LCM of Numerators as per given numbers 21/9, 56/75, 23/17 is
LCM of Numerators i.e. for 21,56,23 is 3864
GCF of denominators i.e. for 9,75,17 is 1.
Thus, LCM of Fractions is 3864.Finally, LCM of Fractions for 21/9, 56/75, 23/17 is 3864.