Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 31/89, 84/16, 55/48, 33/415 quickly i.e. 143220 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 31/89, 84/16, 55/48, 33/415 is 143220.
LCM(31/89, 84/16, 55/48, 33/415) = 143220
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 31/89,84/16,55/48,33/415
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 31,84,55,33
Least Common Multiple of Numerators i.e. LCM of 31,84,55,33 is 143220.
GCF of Denominators means GCF of 89,16,48,415 as per the given fractions.
GCF of 89,16,48,415 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 31,84,55,33
3 | 31, 84, 55, 33 |
11 | 31, 28, 55, 11 |
31, 28, 5, 1 |
∴ So the LCM of the given numbers is 3 x 11 x 31 x 28 x 5 x 1 = 143220
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 31,84,55,33 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,84,55,33) = 1
common factors(in case of two or more numbers have common factors) = 33
GCF(31,84,55,33) x common factors =1 x 33 = 33
LCM(31,84,55,33) = ( 31 × 84 × 55 × 33 ) / 33
LCM(31,84,55,33) = 4726260 / 33
LCM(31,84,55,33) = 143220
Lets's calculate GCF of 89,16,48,415
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 143220/1
Therefore the LCM of Fractions 31/89,84/16,55/48,33/415 is 143220
Factors of 89
List of positive integer factors of 89 that divides 89 without a remainder.
1,89
Factors of 16
List of positive integer factors of 16 that divides 16 without a remainder.
1,2,4,8,16
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 415
List of positive integer factors of 415 that divides 415 without a remainder.
1,5,83,415
Greatest Common Factor
We found the factors 89,16,48,415 . The biggest common factor number is the GCF number.
So the greatest common factor 89,16,48,415 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 31/89, 84/16, 55/48, 33/415?
Answer: LCM of Numerators as per given numbers 31/89, 84/16, 55/48, 33/415 is
LCM of Numerators i.e. for 31,84,55,33 is 143220
GCF of denominators i.e. for 89,16,48,415 is 1.
Thus, LCM of Fractions is 143220.Finally, LCM of Fractions for 31/89, 84/16, 55/48, 33/415 is 143220.