Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 42/28, 74/81, 96/46, 78/749 quickly i.e. 323232 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 42/28, 74/81, 96/46, 78/749 is 323232.
LCM(42/28, 74/81, 96/46, 78/749) = 323232
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 42/28,74/81,96/46,78/749
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 42,74,96,78
Least Common Multiple of Numerators i.e. LCM of 42,74,96,78 is 323232.
GCF of Denominators means GCF of 28,81,46,749 as per the given fractions.
GCF of 28,81,46,749 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 42,74,96,78
2 | 42, 74, 96, 78 |
3 | 21, 37, 48, 39 |
7, 37, 16, 13 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 37 x 16 x 13 = 323232
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 42,74,96,78 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,74,96,78) = 2
common factors(in case of two or more numbers have common factors) = 36
GCF(42,74,96,78) x common factors =2 x 36 = 72
LCM(42,74,96,78) = ( 42 × 74 × 96 × 78 ) / 72
LCM(42,74,96,78) = 23272704 / 72
LCM(42,74,96,78) = 323232
Lets's calculate GCF of 28,81,46,749
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 323232/1
Therefore the LCM of Fractions 42/28,74/81,96/46,78/749 is 323232
Factors of 28
List of positive integer factors of 28 that divides 28 without a remainder.
1,2,4,7,14,28
Factors of 81
List of positive integer factors of 81 that divides 81 without a remainder.
1,3,9,27,81
Factors of 46
List of positive integer factors of 46 that divides 46 without a remainder.
1,2,23,46
Factors of 749
List of positive integer factors of 749 that divides 749 without a remainder.
1,7,107,749
Greatest Common Factor
We found the factors 28,81,46,749 . The biggest common factor number is the GCF number.
So the greatest common factor 28,81,46,749 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 42/28, 74/81, 96/46, 78/749?
Answer: LCM of Numerators as per given numbers 42/28, 74/81, 96/46, 78/749 is
LCM of Numerators i.e. for 42,74,96,78 is 323232
GCF of denominators i.e. for 28,81,46,749 is 1.
Thus, LCM of Fractions is 323232.Finally, LCM of Fractions for 42/28, 74/81, 96/46, 78/749 is 323232.