Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 15/67, 80/77, 28/16, 91/192 quickly i.e. 21840 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 15/67, 80/77, 28/16, 91/192 is 21840.
LCM(15/67, 80/77, 28/16, 91/192) = 21840
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 15/67,80/77,28/16,91/192
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 15,80,28,91
Least Common Multiple of Numerators i.e. LCM of 15,80,28,91 is 21840.
GCF of Denominators means GCF of 67,77,16,192 as per the given fractions.
GCF of 67,77,16,192 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 15,80,28,91
2 | 15, 80, 28, 91 |
2 | 15, 40, 14, 91 |
5 | 15, 20, 7, 91 |
7 | 3, 4, 7, 91 |
3, 4, 1, 13 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 7 x 3 x 4 x 1 x 13 = 21840
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 15,80,28,91 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(15,80,28,91) = 1
common factors(in case of two or more numbers have common factors) = 140
GCF(15,80,28,91) x common factors =1 x 140 = 140
LCM(15,80,28,91) = ( 15 × 80 × 28 × 91 ) / 140
LCM(15,80,28,91) = 3057600 / 140
LCM(15,80,28,91) = 21840
Lets's calculate GCF of 67,77,16,192
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 21840/1
Therefore the LCM of Fractions 15/67,80/77,28/16,91/192 is 21840
Factors of 67
List of positive integer factors of 67 that divides 67 without a remainder.
1,67
Factors of 77
List of positive integer factors of 77 that divides 77 without a remainder.
1,7,11,77
Factors of 16
List of positive integer factors of 16 that divides 16 without a remainder.
1,2,4,8,16
Factors of 192
List of positive integer factors of 192 that divides 192 without a remainder.
1,2,3,4,6,8,12,16,24,32,48,64,96,192
Greatest Common Factor
We found the factors 67,77,16,192 . The biggest common factor number is the GCF number.
So the greatest common factor 67,77,16,192 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 15/67, 80/77, 28/16, 91/192?
Answer: LCM of Numerators as per given numbers 15/67, 80/77, 28/16, 91/192 is
LCM of Numerators i.e. for 15,80,28,91 is 21840
GCF of denominators i.e. for 67,77,16,192 is 1.
Thus, LCM of Fractions is 21840.Finally, LCM of Fractions for 15/67, 80/77, 28/16, 91/192 is 21840.