Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 40/24, 42/22, 31/44, 24/394 quickly i.e. 13020 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 40/24, 42/22, 31/44, 24/394 is 13020.
LCM(40/24, 42/22, 31/44, 24/394) = 13020
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 40/24,42/22,31/44,24/394
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 40,42,31,24
Least Common Multiple of Numerators i.e. LCM of 40,42,31,24 is 26040.
GCF of Denominators means GCF of 24,22,44,394 as per the given fractions.
GCF of 24,22,44,394 is 2 as it is the largest common factor for these numbers.
Lets's calculate LCM of 40,42,31,24
2 | 40, 42, 31, 24 |
2 | 20, 21, 31, 12 |
2 | 10, 21, 31, 6 |
3 | 5, 21, 31, 3 |
5, 7, 31, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 5 x 7 x 31 x 1 = 26040
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 40,42,31,24 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,42,31,24) = 1
common factors(in case of two or more numbers have common factors) = 48
GCF(40,42,31,24) x common factors =1 x 48 = 48
LCM(40,42,31,24) = ( 40 × 42 × 31 × 24 ) / 48
LCM(40,42,31,24) = 1249920 / 48
LCM(40,42,31,24) = 26040
Lets's calculate GCF of 24,22,44,394
2 | 24, 22, 44, 394 |
12, 11, 22, 197 |
∴ So the GCF of the given numbers is 2 = 2
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 26040/2
Therefore the LCM of Fractions 40/24,42/22,31/44,24/394 is 13020
Factors of 24
List of positive integer factors of 24 that divides 24 without a remainder.
1,2,3,4,6,8,12,24
Factors of 22
List of positive integer factors of 22 that divides 22 without a remainder.
1,2,11,22
Factors of 44
List of positive integer factors of 44 that divides 44 without a remainder.
1,2,4,11,22,44
Factors of 394
List of positive integer factors of 394 that divides 394 without a remainder.
1,2,197,394
Greatest Common Factor
We found the factors 24,22,44,394 . The biggest common factor number is the GCF number.
So the greatest common factor 24,22,44,394 is 2.
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 40/24, 42/22, 31/44, 24/394?
Answer: LCM of Numerators as per given numbers 40/24, 42/22, 31/44, 24/394 is
LCM of Numerators i.e. for 40,42,31,24 is 26040
GCF of denominators i.e. for 24,22,44,394 is 2.
Thus, LCM of Fractions is 13020.Finally, LCM of Fractions for 40/24, 42/22, 31/44, 24/394 is 13020.