Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 20/85, 16/64, 28/18, 77/385 quickly i.e. 6160 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 20/85, 16/64, 28/18, 77/385 is 6160.
LCM(20/85, 16/64, 28/18, 77/385) = 6160
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 20/85,16/64,28/18,77/385
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 20,16,28,77
Least Common Multiple of Numerators i.e. LCM of 20,16,28,77 is 6160.
GCF of Denominators means GCF of 85,64,18,385 as per the given fractions.
GCF of 85,64,18,385 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 20,16,28,77
2 | 20, 16, 28, 77 |
2 | 10, 8, 14, 77 |
7 | 5, 4, 7, 77 |
5, 4, 1, 11 |
∴ So the LCM of the given numbers is 2 x 2 x 7 x 5 x 4 x 1 x 11 = 6160
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 20,16,28,77 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(20,16,28,77) = 1
common factors(in case of two or more numbers have common factors) = 112
GCF(20,16,28,77) x common factors =1 x 112 = 112
LCM(20,16,28,77) = ( 20 × 16 × 28 × 77 ) / 112
LCM(20,16,28,77) = 689920 / 112
LCM(20,16,28,77) = 6160
Lets's calculate GCF of 85,64,18,385
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 6160/1
Therefore the LCM of Fractions 20/85,16/64,28/18,77/385 is 6160
Factors of 85
List of positive integer factors of 85 that divides 85 without a remainder.
1,5,17,85
Factors of 64
List of positive integer factors of 64 that divides 64 without a remainder.
1,2,4,8,16,32,64
Factors of 18
List of positive integer factors of 18 that divides 18 without a remainder.
1,2,3,6,9,18
Factors of 385
List of positive integer factors of 385 that divides 385 without a remainder.
1,5,7,11,35,55,77,385
Greatest Common Factor
We found the factors 85,64,18,385 . The biggest common factor number is the GCF number.
So the greatest common factor 85,64,18,385 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 20/85, 16/64, 28/18, 77/385?
Answer: LCM of Numerators as per given numbers 20/85, 16/64, 28/18, 77/385 is
LCM of Numerators i.e. for 20,16,28,77 is 6160
GCF of denominators i.e. for 85,64,18,385 is 1.
Thus, LCM of Fractions is 6160.Finally, LCM of Fractions for 20/85, 16/64, 28/18, 77/385 is 6160.