Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 18/12, 40/66, 66/44, 44/123 quickly i.e. 3960 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 18/12, 40/66, 66/44, 44/123 is 3960.
LCM(18/12, 40/66, 66/44, 44/123) = 3960
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 18/12,40/66,66/44,44/123
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 18,40,66,44
Least Common Multiple of Numerators i.e. LCM of 18,40,66,44 is 3960.
GCF of Denominators means GCF of 12,66,44,123 as per the given fractions.
GCF of 12,66,44,123 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 18,40,66,44
2 | 18, 40, 66, 44 |
2 | 9, 20, 33, 22 |
3 | 9, 10, 33, 11 |
11 | 3, 10, 11, 11 |
3, 10, 1, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 11 x 3 x 10 x 1 x 1 = 3960
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 18,40,66,44 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(18,40,66,44) = 2
common factors(in case of two or more numbers have common factors) = 264
GCF(18,40,66,44) x common factors =2 x 264 = 528
LCM(18,40,66,44) = ( 18 × 40 × 66 × 44 ) / 528
LCM(18,40,66,44) = 2090880 / 528
LCM(18,40,66,44) = 3960
Lets's calculate GCF of 12,66,44,123
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 3960/1
Therefore the LCM of Fractions 18/12,40/66,66/44,44/123 is 3960
Factors of 12
List of positive integer factors of 12 that divides 12 without a remainder.
1,2,3,4,6,12
Factors of 66
List of positive integer factors of 66 that divides 66 without a remainder.
1,2,3,6,11,22,33,66
Factors of 44
List of positive integer factors of 44 that divides 44 without a remainder.
1,2,4,11,22,44
Factors of 123
List of positive integer factors of 123 that divides 123 without a remainder.
1,3,41,123
Greatest Common Factor
We found the factors 12,66,44,123 . The biggest common factor number is the GCF number.
So the greatest common factor 12,66,44,123 is 1.
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 18/12, 40/66, 66/44, 44/123?
Answer: LCM of Numerators as per given numbers 18/12, 40/66, 66/44, 44/123 is
LCM of Numerators i.e. for 18,40,66,44 is 3960
GCF of denominators i.e. for 12,66,44,123 is 1.
Thus, LCM of Fractions is 3960.Finally, LCM of Fractions for 18/12, 40/66, 66/44, 44/123 is 3960.