Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 65/54, 71/30, 189/48 quickly i.e. 872235/6 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 65/54, 71/30, 189/48 is 872235/6.
LCM(65/54, 71/30, 189/48) = 872235/6
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 65/54,71/30,189/48
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 65,71,189
Least Common Multiple of Numerators i.e. LCM of 65,71,189 is 872235.
GCF of Denominators means GCF of 54,30,48 as per the given fractions.
GCF of 54,30,48 is 6 as it is the largest common factor for these numbers.
Lets's calculate LCM of 65,71,189
Given numbers has no common factors except 1. So, there LCM is their product i.e 872235
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 65,71,189 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(65,71,189) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(65,71,189) x common factors =1 x 1 = 1
LCM(65,71,189) = ( 65 × 71 × 189 ) / 1
LCM(65,71,189) = 872235 / 1
LCM(65,71,189) = 872235
Lets's calculate GCF of 54,30,48
2 | 54, 30, 48 |
3 | 27, 15, 24 |
9, 5, 8 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 872235/6
Therefore the LCM of Fractions 65/54,71/30,189/48 is 872235/6
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 30
List of positive integer factors of 30 that divides 30 without a remainder.
1,2,3,5,6,10,15,30
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
Greatest Common Factor
We found the factors 54,30,48 . The biggest common factor number is the GCF number.
So the greatest common factor 54,30,48 is 6.
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 65/54, 71/30, 189/48?
Answer: LCM of Numerators as per given numbers 65/54, 71/30, 189/48 is
LCM of Numerators i.e. for 65,71,189 is 872235
GCF of denominators i.e. for 54,30,48 is 6.
Thus, LCM of Fractions is 872235/6.Finally, LCM of Fractions for 65/54, 71/30, 189/48 is 872235/6.