Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 83/24, 42/82, 30/74, 56/67 quickly i.e. 69720 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 83/24, 42/82, 30/74, 56/67 is 69720.
LCM(83/24, 42/82, 30/74, 56/67) = 69720
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 83/24,42/82,30/74,56/67
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 83,42,30,56
Least Common Multiple of Numerators i.e. LCM of 83,42,30,56 is 69720.
GCF of Denominators means GCF of 24,82,74,67 as per the given fractions.
GCF of 24,82,74,67 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 83,42,30,56
2 | 83, 42, 30, 56 |
3 | 83, 21, 15, 28 |
7 | 83, 7, 5, 28 |
83, 1, 5, 4 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 83 x 1 x 5 x 4 = 69720
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 83,42,30,56 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(83,42,30,56) = 1
common factors(in case of two or more numbers have common factors) = 84
GCF(83,42,30,56) x common factors =1 x 84 = 84
LCM(83,42,30,56) = ( 83 × 42 × 30 × 56 ) / 84
LCM(83,42,30,56) = 5856480 / 84
LCM(83,42,30,56) = 69720
Lets's calculate GCF of 24,82,74,67
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 69720/1
Therefore the LCM of Fractions 83/24,42/82,30/74,56/67 is 69720
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 82
List of positive integer factors of 82 that divides 82 without a remainder.
1,2,41,82
Factors of 74
List of positive integer factors of 74 that divides 74 without a remainder.
1,2,37,74
Factors of 67
List of positive integer factors of 67 that divides 67 without a remainder.
1,67
Greatest Common Factor
We found the factors 24,82,74,67 . The biggest common factor number is the GCF number.
So the greatest common factor 24,82,74,67 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 83/24, 42/82, 30/74, 56/67?
Answer: LCM of Numerators as per given numbers 83/24, 42/82, 30/74, 56/67 is
LCM of Numerators i.e. for 83,42,30,56 is 69720
GCF of denominators i.e. for 24,82,74,67 is 1.
Thus, LCM of Fractions is 69720.Finally, LCM of Fractions for 83/24, 42/82, 30/74, 56/67 is 69720.