Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 9/87, 75/708, 45/231 quickly i.e. 75 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 9/87, 75/708, 45/231 is 75.
LCM(9/87, 75/708, 45/231) = 75
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 9/87,75/708,45/231
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 9,75,45
Least Common Multiple of Numerators i.e. LCM of 9,75,45 is 225.
GCF of Denominators means GCF of 87,708,231 as per the given fractions.
GCF of 87,708,231 is 3 as it is the largest common factor for these numbers.
Lets's calculate LCM of 9,75,45
3 | 9, 75, 45 |
3 | 3, 25, 15 |
5 | 1, 25, 5 |
1, 1, 5 |
∴ So the LCM of the given numbers is 3 x 3 x 5 x 1 x 1 x 5 = 225
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 9,75,45 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(9,75,45) = 3
common factors(in case of two or more numbers have common factors) = 45
GCF(9,75,45) x common factors =3 x 45 = 135
LCM(9,75,45) = ( 9 × 75 × 45 ) / 135
LCM(9,75,45) = 30375 / 135
LCM(9,75,45) = 225
Lets's calculate GCF of 87,708,231
3 | 87, 708, 231 |
29, 236, 77 |
∴ So the GCF of the given numbers is 3 = 3
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 225/3
Therefore the LCM of Fractions 9/87,75/708,45/231 is 75
Factors of 87
List of positive integer factors of 87 that divides 87 without a remainder.
1,3,29,87
Factors of 708
List of positive integer factors of 708 that divides 708 without a remainder.
1,2,3,4,6,12,59,118,177,236,354,708
Factors of 231
List of positive integer factors of 231 that divides 231 without a remainder.
1,3,7,11,21,33,77,231
Greatest Common Factor
We found the factors 87,708,231 . The biggest common factor number is the GCF number.
So the greatest common factor 87,708,231 is 3.
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 9/87, 75/708, 45/231?
Answer: LCM of Numerators as per given numbers 9/87, 75/708, 45/231 is
LCM of Numerators i.e. for 9,75,45 is 225
GCF of denominators i.e. for 87,708,231 is 3.
Thus, LCM of Fractions is 75.Finally, LCM of Fractions for 9/87, 75/708, 45/231 is 75.