Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 84/54, 27/33, 243/213 quickly i.e. 2268 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 84/54, 27/33, 243/213 is 2268.
LCM(84/54, 27/33, 243/213) = 2268
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 84/54,27/33,243/213
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 84,27,243
Least Common Multiple of Numerators i.e. LCM of 84,27,243 is 6804.
GCF of Denominators means GCF of 54,33,213 as per the given fractions.
GCF of 54,33,213 is 3 as it is the largest common factor for these numbers.
Lets's calculate LCM of 84,27,243
3 | 84, 27, 243 |
3 | 28, 9, 81 |
3 | 28, 3, 27 |
28, 1, 9 |
∴ So the LCM of the given numbers is 3 x 3 x 3 x 28 x 1 x 9 = 6804
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 84,27,243 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,27,243) = 3
common factors(in case of two or more numbers have common factors) = 27
GCF(84,27,243) x common factors =3 x 27 = 81
LCM(84,27,243) = ( 84 × 27 × 243 ) / 81
LCM(84,27,243) = 551124 / 81
LCM(84,27,243) = 6804
Lets's calculate GCF of 54,33,213
3 | 54, 33, 213 |
18, 11, 71 |
∴ So the GCF of the given numbers is 3 = 3
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 6804/3
Therefore the LCM of Fractions 84/54,27/33,243/213 is 2268
Factors of 54
List of positive integer factors of 54 that divides 54 without a remainder.
1,2,3,6,9,18,27,54
Factors of 33
List of positive integer factors of 33 that divides 33 without a remainder.
1,3,11,33
Factors of 213
List of positive integer factors of 213 that divides 213 without a remainder.
1,3,71,213
Greatest Common Factor
We found the factors 54,33,213 . The biggest common factor number is the GCF number.
So the greatest common factor 54,33,213 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 84/54, 27/33, 243/213?
Answer: LCM of Numerators as per given numbers 84/54, 27/33, 243/213 is
LCM of Numerators i.e. for 84,27,243 is 6804
GCF of denominators i.e. for 54,33,213 is 3.
Thus, LCM of Fractions is 2268.Finally, LCM of Fractions for 84/54, 27/33, 243/213 is 2268.