Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 345/243, 420/170, 305/521 quickly i.e. 589260 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 345/243, 420/170, 305/521 is 589260.
LCM(345/243, 420/170, 305/521) = 589260
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 345/243,420/170,305/521
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 345,420,305
Least Common Multiple of Numerators i.e. LCM of 345,420,305 is 589260.
GCF of Denominators means GCF of 243,170,521 as per the given fractions.
GCF of 243,170,521 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 345,420,305
3 | 345, 420, 305 |
5 | 115, 140, 305 |
23, 28, 61 |
∴ So the LCM of the given numbers is 3 x 5 x 23 x 28 x 61 = 589260
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 345,420,305 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(345,420,305) = 5
common factors(in case of two or more numbers have common factors) = 15
GCF(345,420,305) x common factors =5 x 15 = 75
LCM(345,420,305) = ( 345 × 420 × 305 ) / 75
LCM(345,420,305) = 44194500 / 75
LCM(345,420,305) = 589260
Lets's calculate GCF of 243,170,521
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 589260/1
Therefore the LCM of Fractions 345/243,420/170,305/521 is 589260
Factors of 243
List of positive integer factors of 243 that divides 243 without a remainder.
1,3,9,27,81,243
Factors of 170
List of positive integer factors of 170 that divides 170 without a remainder.
1,2,5,10,17,34,85,170
Factors of 521
List of positive integer factors of 521 that divides 521 without a remainder.
1,521
Greatest Common Factor
We found the factors 243,170,521 . The biggest common factor number is the GCF number.
So the greatest common factor 243,170,521 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 345/243, 420/170, 305/521?
Answer: LCM of Numerators as per given numbers 345/243, 420/170, 305/521 is
LCM of Numerators i.e. for 345,420,305 is 589260
GCF of denominators i.e. for 243,170,521 is 1.
Thus, LCM of Fractions is 589260.Finally, LCM of Fractions for 345/243, 420/170, 305/521 is 589260.