Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 72/89, 87/23, 40/37, 765/66 quickly i.e. 177480 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 72/89, 87/23, 40/37, 765/66 is 177480.
LCM(72/89, 87/23, 40/37, 765/66) = 177480
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 72/89,87/23,40/37,765/66
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 72,87,40,765
Least Common Multiple of Numerators i.e. LCM of 72,87,40,765 is 177480.
GCF of Denominators means GCF of 89,23,37,66 as per the given fractions.
GCF of 89,23,37,66 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 72,87,40,765
2 | 72, 87, 40, 765 |
2 | 36, 87, 20, 765 |
2 | 18, 87, 10, 765 |
3 | 9, 87, 5, 765 |
3 | 3, 29, 5, 255 |
5 | 1, 29, 5, 85 |
1, 29, 1, 17 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 3 x 5 x 1 x 29 x 1 x 17 = 177480
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 72,87,40,765 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(72,87,40,765) = 1
common factors(in case of two or more numbers have common factors) = 1080
GCF(72,87,40,765) x common factors =1 x 1080 = 1080
LCM(72,87,40,765) = ( 72 × 87 × 40 × 765 ) / 1080
LCM(72,87,40,765) = 191678400 / 1080
LCM(72,87,40,765) = 177480
Lets's calculate GCF of 89,23,37,66
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 177480/1
Therefore the LCM of Fractions 72/89,87/23,40/37,765/66 is 177480
Factors of 89
List of positive integer factors of 89 that divides 89 without a remainder.
1,89
Factors of 23
List of positive integer factors of 23 that divides 23 without a remainder.
1,23
Factors of 37
List of positive integer factors of 37 that divides 37 without a remainder.
1,37
Factors of 66
List of positive integer factors of 66 that divides 66 without a remainder.
1,2,3,6,11,22,33,66
Greatest Common Factor
We found the factors 89,23,37,66 . The biggest common factor number is the GCF number.
So the greatest common factor 89,23,37,66 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 72/89, 87/23, 40/37, 765/66?
Answer: LCM of Numerators as per given numbers 72/89, 87/23, 40/37, 765/66 is
LCM of Numerators i.e. for 72,87,40,765 is 177480
GCF of denominators i.e. for 89,23,37,66 is 1.
Thus, LCM of Fractions is 177480.Finally, LCM of Fractions for 72/89, 87/23, 40/37, 765/66 is 177480.