Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 36/80, 60/14, 68/30, 67/684 quickly i.e. 102510 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 36/80, 60/14, 68/30, 67/684 is 102510.
LCM(36/80, 60/14, 68/30, 67/684) = 102510
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 36/80,60/14,68/30,67/684
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 36,60,68,67
Least Common Multiple of Numerators i.e. LCM of 36,60,68,67 is 205020.
GCF of Denominators means GCF of 80,14,30,684 as per the given fractions.
GCF of 80,14,30,684 is 2 as it is the largest common factor for these numbers.
Lets's calculate LCM of 36,60,68,67
2 | 36, 60, 68, 67 |
2 | 18, 30, 34, 67 |
3 | 9, 15, 17, 67 |
3, 5, 17, 67 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 5 x 17 x 67 = 205020
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 36,60,68,67 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(36,60,68,67) = 1
common factors(in case of two or more numbers have common factors) = 48
GCF(36,60,68,67) x common factors =1 x 48 = 48
LCM(36,60,68,67) = ( 36 × 60 × 68 × 67 ) / 48
LCM(36,60,68,67) = 9840960 / 48
LCM(36,60,68,67) = 205020
Lets's calculate GCF of 80,14,30,684
2 | 80, 14, 30, 684 |
40, 7, 15, 342 |
∴ So the GCF of the given numbers is 2 = 2
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 205020/2
Therefore the LCM of Fractions 36/80,60/14,68/30,67/684 is 102510
Factors of 80
List of positive integer factors of 80 that divides 80 without a remainder.
1,2,4,5,8,10,16,20,40,80
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1,2,7,14
Factors of 30
List of positive integer factors of 30 that divides 30 without a remainder.
1,2,3,5,6,10,15,30
Factors of 684
List of positive integer factors of 684 that divides 684 without a remainder.
1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Greatest Common Factor
We found the factors 80,14,30,684 . The biggest common factor number is the GCF number.
So the greatest common factor 80,14,30,684 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 36/80, 60/14, 68/30, 67/684?
Answer: LCM of Numerators as per given numbers 36/80, 60/14, 68/30, 67/684 is
LCM of Numerators i.e. for 36,60,68,67 is 205020
GCF of denominators i.e. for 80,14,30,684 is 2.
Thus, LCM of Fractions is 102510.Finally, LCM of Fractions for 36/80, 60/14, 68/30, 67/684 is 102510.