Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 75/414, 396/471, 459/421 quickly i.e. 504900 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 75/414, 396/471, 459/421 is 504900.
LCM(75/414, 396/471, 459/421) = 504900
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 75/414,396/471,459/421
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 75,396,459
Least Common Multiple of Numerators i.e. LCM of 75,396,459 is 504900.
GCF of Denominators means GCF of 414,471,421 as per the given fractions.
GCF of 414,471,421 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 75,396,459
3 | 75, 396, 459 |
3 | 25, 132, 153 |
25, 44, 51 |
∴ So the LCM of the given numbers is 3 x 3 x 25 x 44 x 51 = 504900
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 75,396,459 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,396,459) = 3
common factors(in case of two or more numbers have common factors) = 9
GCF(75,396,459) x common factors =3 x 9 = 27
LCM(75,396,459) = ( 75 × 396 × 459 ) / 27
LCM(75,396,459) = 13632300 / 27
LCM(75,396,459) = 504900
Lets's calculate GCF of 414,471,421
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 504900/1
Therefore the LCM of Fractions 75/414,396/471,459/421 is 504900
Factors of 414
List of positive integer factors of 414 that divides 414 without a remainder.
1,2,3,6,9,18,23,46,69,138,207,414
Factors of 471
List of positive integer factors of 471 that divides 471 without a remainder.
1,3,157,471
Factors of 421
List of positive integer factors of 421 that divides 421 without a remainder.
1,421
Greatest Common Factor
We found the factors 414,471,421 . The biggest common factor number is the GCF number.
So the greatest common factor 414,471,421 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 75/414, 396/471, 459/421?
Answer: LCM of Numerators as per given numbers 75/414, 396/471, 459/421 is
LCM of Numerators i.e. for 75,396,459 is 504900
GCF of denominators i.e. for 414,471,421 is 1.
Thus, LCM of Fractions is 504900.Finally, LCM of Fractions for 75/414, 396/471, 459/421 is 504900.