Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 152/20, 418/74, 309/321 quickly i.e. 516648 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 152/20, 418/74, 309/321 is 516648.
LCM(152/20, 418/74, 309/321) = 516648
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 152/20,418/74,309/321
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 152,418,309
Least Common Multiple of Numerators i.e. LCM of 152,418,309 is 516648.
GCF of Denominators means GCF of 20,74,321 as per the given fractions.
GCF of 20,74,321 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 152,418,309
2 | 152, 418, 309 |
19 | 76, 209, 309 |
4, 11, 309 |
∴ So the LCM of the given numbers is 2 x 19 x 4 x 11 x 309 = 516648
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 152,418,309 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(152,418,309) = 1
common factors(in case of two or more numbers have common factors) = 38
GCF(152,418,309) x common factors =1 x 38 = 38
LCM(152,418,309) = ( 152 × 418 × 309 ) / 38
LCM(152,418,309) = 19632624 / 38
LCM(152,418,309) = 516648
Lets's calculate GCF of 20,74,321
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 516648/1
Therefore the LCM of Fractions 152/20,418/74,309/321 is 516648
Factors of 20
List of positive integer factors of 20 that divides 20 without a remainder.
1,2,4,5,10,20
Factors of 74
List of positive integer factors of 74 that divides 74 without a remainder.
1,2,37,74
Factors of 321
List of positive integer factors of 321 that divides 321 without a remainder.
1,3,107,321
Greatest Common Factor
We found the factors 20,74,321 . The biggest common factor number is the GCF number.
So the greatest common factor 20,74,321 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 152/20, 418/74, 309/321?
Answer: LCM of Numerators as per given numbers 152/20, 418/74, 309/321 is
LCM of Numerators i.e. for 152,418,309 is 516648
GCF of denominators i.e. for 20,74,321 is 1.
Thus, LCM of Fractions is 516648.Finally, LCM of Fractions for 152/20, 418/74, 309/321 is 516648.