Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 75/46, 12/16, 29/84, 87/866 quickly i.e. 4350 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 75/46, 12/16, 29/84, 87/866 is 4350.
LCM(75/46, 12/16, 29/84, 87/866) = 4350
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 75/46,12/16,29/84,87/866
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 75,12,29,87
Least Common Multiple of Numerators i.e. LCM of 75,12,29,87 is 8700.
GCF of Denominators means GCF of 46,16,84,866 as per the given fractions.
GCF of 46,16,84,866 is 2 as it is the largest common factor for these numbers.
Lets's calculate LCM of 75,12,29,87
3 | 75, 12, 29, 87 |
29 | 25, 4, 29, 29 |
25, 4, 1, 1 |
∴ So the LCM of the given numbers is 3 x 29 x 25 x 4 x 1 x 1 = 8700
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 75,12,29,87 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,12,29,87) = 1
common factors(in case of two or more numbers have common factors) = 261
GCF(75,12,29,87) x common factors =1 x 261 = 261
LCM(75,12,29,87) = ( 75 × 12 × 29 × 87 ) / 261
LCM(75,12,29,87) = 2270700 / 261
LCM(75,12,29,87) = 8700
Lets's calculate GCF of 46,16,84,866
2 | 46, 16, 84, 866 |
23, 8, 42, 433 |
∴ So the GCF of the given numbers is 2 = 2
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 8700/2
Therefore the LCM of Fractions 75/46,12/16,29/84,87/866 is 4350
Factors of 46
List of positive integer factors of 46 that divides 46 without a remainder.
1,2,23,46
Factors of 16
List of positive integer factors of 16 that divides 16 without a remainder.
1,2,4,8,16
Factors of 84
List of positive integer factors of 84 that divides 84 without a remainder.
1,2,3,4,6,7,12,14,21,28,42,84
Factors of 866
List of positive integer factors of 866 that divides 866 without a remainder.
1,2,433,866
Greatest Common Factor
We found the factors 46,16,84,866 . The biggest common factor number is the GCF number.
So the greatest common factor 46,16,84,866 is 2.
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 75/46, 12/16, 29/84, 87/866?
Answer: LCM of Numerators as per given numbers 75/46, 12/16, 29/84, 87/866 is
LCM of Numerators i.e. for 75,12,29,87 is 8700
GCF of denominators i.e. for 46,16,84,866 is 2.
Thus, LCM of Fractions is 4350.Finally, LCM of Fractions for 75/46, 12/16, 29/84, 87/866 is 4350.