Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 258/27, 178/51, 330/21 quickly i.e. 420970 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 258/27, 178/51, 330/21 is 420970.
LCM(258/27, 178/51, 330/21) = 420970
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 258/27,178/51,330/21
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 258,178,330
Least Common Multiple of Numerators i.e. LCM of 258,178,330 is 1262910.
GCF of Denominators means GCF of 27,51,21 as per the given fractions.
GCF of 27,51,21 is 3 as it is the largest common factor for these numbers.
Lets's calculate LCM of 258,178,330
2 | 258, 178, 330 |
3 | 129, 89, 165 |
43, 89, 55 |
∴ So the LCM of the given numbers is 2 x 3 x 43 x 89 x 55 = 1262910
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 258,178,330 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(258,178,330) = 2
common factors(in case of two or more numbers have common factors) = 6
GCF(258,178,330) x common factors =2 x 6 = 12
LCM(258,178,330) = ( 258 × 178 × 330 ) / 12
LCM(258,178,330) = 15154920 / 12
LCM(258,178,330) = 1262910
Lets's calculate GCF of 27,51,21
3 | 27, 51, 21 |
9, 17, 7 |
∴ So the GCF of the given numbers is 3 = 3
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 1262910/3
Therefore the LCM of Fractions 258/27,178/51,330/21 is 420970
Factors of 27
List of positive integer factors of 27 that divides 27 without a remainder.
1,3,9,27
Factors of 51
List of positive integer factors of 51 that divides 51 without a remainder.
1,3,17,51
Factors of 21
List of positive integer factors of 21 that divides 21 without a remainder.
1,3,7,21
Greatest Common Factor
We found the factors 27,51,21 . The biggest common factor number is the GCF number.
So the greatest common factor 27,51,21 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 258/27, 178/51, 330/21?
Answer: LCM of Numerators as per given numbers 258/27, 178/51, 330/21 is
LCM of Numerators i.e. for 258,178,330 is 1262910
GCF of denominators i.e. for 27,51,21 is 3.
Thus, LCM of Fractions is 420970.Finally, LCM of Fractions for 258/27, 178/51, 330/21 is 420970.