Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 96/28, 49/14, 11/34, 78/30 quickly i.e. 336336 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 96/28, 49/14, 11/34, 78/30 is 336336.
LCM(96/28, 49/14, 11/34, 78/30) = 336336
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 96/28,49/14,11/34,78/30
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 96,49,11,78
Least Common Multiple of Numerators i.e. LCM of 96,49,11,78 is 672672.
GCF of Denominators means GCF of 28,14,34,30 as per the given fractions.
GCF of 28,14,34,30 is 2 as it is the largest common factor for these numbers.
Lets's calculate LCM of 96,49,11,78
2 | 96, 49, 11, 78 |
3 | 48, 49, 11, 39 |
16, 49, 11, 13 |
∴ So the LCM of the given numbers is 2 x 3 x 16 x 49 x 11 x 13 = 672672
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 96,49,11,78 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(96,49,11,78) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(96,49,11,78) x common factors =1 x 6 = 6
LCM(96,49,11,78) = ( 96 × 49 × 11 × 78 ) / 6
LCM(96,49,11,78) = 4036032 / 6
LCM(96,49,11,78) = 672672
Lets's calculate GCF of 28,14,34,30
2 | 28, 14, 34, 30 |
14, 7, 17, 15 |
∴ So the GCF of the given numbers is 2 = 2
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 672672/2
Therefore the LCM of Fractions 96/28,49/14,11/34,78/30 is 336336
Factors of 28
List of positive integer factors of 28 that divides 28 without a remainder.
1,2,4,7,14,28
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1,2,7,14
Factors of 34
List of positive integer factors of 34 that divides 34 without a remainder.
1,2,17,34
Factors of 30
List of positive integer factors of 30 that divides 30 without a remainder.
1,2,3,5,6,10,15,30
Greatest Common Factor
We found the factors 28,14,34,30 . The biggest common factor number is the GCF number.
So the greatest common factor 28,14,34,30 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 96/28, 49/14, 11/34, 78/30?
Answer: LCM of Numerators as per given numbers 96/28, 49/14, 11/34, 78/30 is
LCM of Numerators i.e. for 96,49,11,78 is 672672
GCF of denominators i.e. for 28,14,34,30 is 2.
Thus, LCM of Fractions is 336336.Finally, LCM of Fractions for 96/28, 49/14, 11/34, 78/30 is 336336.