Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 89/48, 90/99, 72/90, 12/75 quickly i.e. 10680 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 89/48, 90/99, 72/90, 12/75 is 10680.
LCM(89/48, 90/99, 72/90, 12/75) = 10680
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 89/48,90/99,72/90,12/75
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 89,90,72,12
Least Common Multiple of Numerators i.e. LCM of 89,90,72,12 is 32040.
GCF of Denominators means GCF of 48,99,90,75 as per the given fractions.
GCF of 48,99,90,75 is 3 as it is the largest common factor for these numbers.
Lets's calculate LCM of 89,90,72,12
2 | 89, 90, 72, 12 |
2 | 89, 45, 36, 6 |
3 | 89, 45, 18, 3 |
3 | 89, 15, 6, 1 |
89, 5, 2, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 89 x 5 x 2 x 1 = 32040
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 89,90,72,12 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(89,90,72,12) = 1
common factors(in case of two or more numbers have common factors) = 216
GCF(89,90,72,12) x common factors =1 x 216 = 216
LCM(89,90,72,12) = ( 89 × 90 × 72 × 12 ) / 216
LCM(89,90,72,12) = 6920640 / 216
LCM(89,90,72,12) = 32040
Lets's calculate GCF of 48,99,90,75
3 | 48, 99, 90, 75 |
16, 33, 30, 25 |
∴ So the GCF of the given numbers is 3 = 3
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 32040/3
Therefore the LCM of Fractions 89/48,90/99,72/90,12/75 is 10680
Factors of 48
List of positive integer factors of 48 that divides 48 without a remainder.
1,2,3,4,6,8,12,16,24,48
Factors of 99
List of positive integer factors of 99 that divides 99 without a remainder.
1,3,9,11,33,99
Factors of 90
List of positive integer factors of 90 that divides 90 without a remainder.
1,2,3,5,6,9,10,15,18,30,45,90
Factors of 75
List of positive integer factors of 75 that divides 75 without a remainder.
1,3,5,15,25,75
Greatest Common Factor
We found the factors 48,99,90,75 . The biggest common factor number is the GCF number.
So the greatest common factor 48,99,90,75 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 89/48, 90/99, 72/90, 12/75?
Answer: LCM of Numerators as per given numbers 89/48, 90/99, 72/90, 12/75 is
LCM of Numerators i.e. for 89,90,72,12 is 32040
GCF of denominators i.e. for 48,99,90,75 is 3.
Thus, LCM of Fractions is 10680.Finally, LCM of Fractions for 89/48, 90/99, 72/90, 12/75 is 10680.