Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 96/144, 578/411, 560/459 quickly i.e. 323680 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 96/144, 578/411, 560/459 is 323680.
LCM(96/144, 578/411, 560/459) = 323680
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 96/144,578/411,560/459
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 96,578,560
Least Common Multiple of Numerators i.e. LCM of 96,578,560 is 971040.
GCF of Denominators means GCF of 144,411,459 as per the given fractions.
GCF of 144,411,459 is 3 as it is the largest common factor for these numbers.
Lets's calculate LCM of 96,578,560
2 | 96, 578, 560 |
2 | 48, 289, 280 |
2 | 24, 289, 140 |
2 | 12, 289, 70 |
6, 289, 35 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 6 x 289 x 35 = 971040
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 96,578,560 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(96,578,560) = 2
common factors(in case of two or more numbers have common factors) = 16
GCF(96,578,560) x common factors =2 x 16 = 32
LCM(96,578,560) = ( 96 × 578 × 560 ) / 32
LCM(96,578,560) = 31073280 / 32
LCM(96,578,560) = 971040
Lets's calculate GCF of 144,411,459
3 | 144, 411, 459 |
48, 137, 153 |
∴ So the GCF of the given numbers is 3 = 3
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 971040/3
Therefore the LCM of Fractions 96/144,578/411,560/459 is 323680
Factors of 144
List of positive integer factors of 144 that divides 144 without a remainder.
1,2,3,4,6,8,9,12,16,18,24,36,48,72,144
Factors of 411
List of positive integer factors of 411 that divides 411 without a remainder.
1,3,137,411
Factors of 459
List of positive integer factors of 459 that divides 459 without a remainder.
1,3,9,17,27,51,153,459
Greatest Common Factor
We found the factors 144,411,459 . The biggest common factor number is the GCF number.
So the greatest common factor 144,411,459 is 3.
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 96/144, 578/411, 560/459?
Answer: LCM of Numerators as per given numbers 96/144, 578/411, 560/459 is
LCM of Numerators i.e. for 96,578,560 is 971040
GCF of denominators i.e. for 144,411,459 is 3.
Thus, LCM of Fractions is 323680.Finally, LCM of Fractions for 96/144, 578/411, 560/459 is 323680.