Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 30/82, 53/28, 24/56, 46/840 quickly i.e. 73140 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 30/82, 53/28, 24/56, 46/840 is 73140.
LCM(30/82, 53/28, 24/56, 46/840) = 73140
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 30/82,53/28,24/56,46/840
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 30,53,24,46
Least Common Multiple of Numerators i.e. LCM of 30,53,24,46 is 146280.
GCF of Denominators means GCF of 82,28,56,840 as per the given fractions.
GCF of 82,28,56,840 is 2 as it is the largest common factor for these numbers.
Lets's calculate LCM of 30,53,24,46
2 | 30, 53, 24, 46 |
3 | 15, 53, 12, 23 |
5, 53, 4, 23 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 53 x 4 x 23 = 146280
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 30,53,24,46 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,53,24,46) = 1
common factors(in case of two or more numbers have common factors) = 12
GCF(30,53,24,46) x common factors =1 x 12 = 12
LCM(30,53,24,46) = ( 30 × 53 × 24 × 46 ) / 12
LCM(30,53,24,46) = 1755360 / 12
LCM(30,53,24,46) = 146280
Lets's calculate GCF of 82,28,56,840
2 | 82, 28, 56, 840 |
41, 14, 28, 420 |
∴ So the GCF of the given numbers is 2 = 2
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 146280/2
Therefore the LCM of Fractions 30/82,53/28,24/56,46/840 is 73140
Factors of 82
List of positive integer factors of 82 that divides 82 without a remainder.
1,2,41,82
Factors of 28
List of positive integer factors of 28 that divides 28 without a remainder.
1,2,4,7,14,28
Factors of 56
List of positive integer factors of 56 that divides 56 without a remainder.
1,2,4,7,8,14,28,56
Factors of 840
List of positive integer factors of 840 that divides 840 without a remainder.
1,2,3,4,5,6,7,8,10,12,14,15,20,21,24,28,30,35,40,42,56,60,70,84,105,120,140,168,210,280,420,840
Greatest Common Factor
We found the factors 82,28,56,840 . The biggest common factor number is the GCF number.
So the greatest common factor 82,28,56,840 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 30/82, 53/28, 24/56, 46/840?
Answer: LCM of Numerators as per given numbers 30/82, 53/28, 24/56, 46/840 is
LCM of Numerators i.e. for 30,53,24,46 is 146280
GCF of denominators i.e. for 82,28,56,840 is 2.
Thus, LCM of Fractions is 73140.Finally, LCM of Fractions for 30/82, 53/28, 24/56, 46/840 is 73140.