Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 87/400, 21/532, 665/684 quickly i.e. 57855/4 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 87/400, 21/532, 665/684 is 57855/4.
LCM(87/400, 21/532, 665/684) = 57855/4
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 87/400,21/532,665/684
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 87,21,665
Least Common Multiple of Numerators i.e. LCM of 87,21,665 is 57855.
GCF of Denominators means GCF of 400,532,684 as per the given fractions.
GCF of 400,532,684 is 4 as it is the largest common factor for these numbers.
Lets's calculate LCM of 87,21,665
3 | 87, 21, 665 |
7 | 29, 7, 665 |
29, 1, 95 |
∴ So the LCM of the given numbers is 3 x 7 x 29 x 1 x 95 = 57855
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 87,21,665 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(87,21,665) = 1
common factors(in case of two or more numbers have common factors) = 21
GCF(87,21,665) x common factors =1 x 21 = 21
LCM(87,21,665) = ( 87 × 21 × 665 ) / 21
LCM(87,21,665) = 1214955 / 21
LCM(87,21,665) = 57855
Lets's calculate GCF of 400,532,684
2 | 400, 532, 684 |
2 | 200, 266, 342 |
100, 133, 171 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 57855/4
Therefore the LCM of Fractions 87/400,21/532,665/684 is 57855/4
Factors of 400
List of positive integer factors of 400 that divides 400 without a remainder.
1,2,4,5,8,10,16,20,25,40,50,80,100,200,400
Factors of 532
List of positive integer factors of 532 that divides 532 without a remainder.
1,2,4,7,14,19,28,38,76,133,266,532
Factors of 684
List of positive integer factors of 684 that divides 684 without a remainder.
1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Greatest Common Factor
We found the factors 400,532,684 . The biggest common factor number is the GCF number.
So the greatest common factor 400,532,684 is 4.
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 87/400, 21/532, 665/684?
Answer: LCM of Numerators as per given numbers 87/400, 21/532, 665/684 is
LCM of Numerators i.e. for 87,21,665 is 57855
GCF of denominators i.e. for 400,532,684 is 4.
Thus, LCM of Fractions is 57855/4.Finally, LCM of Fractions for 87/400, 21/532, 665/684 is 57855/4.