Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 72/43, 84/39, 67/20 quickly i.e. 33768 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 72/43, 84/39, 67/20 is 33768.
LCM(72/43, 84/39, 67/20) = 33768
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 72/43,84/39,67/20
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 72,84,67
Least Common Multiple of Numerators i.e. LCM of 72,84,67 is 33768.
GCF of Denominators means GCF of 43,39,20 as per the given fractions.
GCF of 43,39,20 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 72,84,67
2 | 72, 84, 67 |
2 | 36, 42, 67 |
3 | 18, 21, 67 |
6, 7, 67 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 6 x 7 x 67 = 33768
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 72,84,67 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(72,84,67) = 1
common factors(in case of two or more numbers have common factors) = 12
GCF(72,84,67) x common factors =1 x 12 = 12
LCM(72,84,67) = ( 72 × 84 × 67 ) / 12
LCM(72,84,67) = 405216 / 12
LCM(72,84,67) = 33768
Lets's calculate GCF of 43,39,20
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 33768/1
Therefore the LCM of Fractions 72/43,84/39,67/20 is 33768
Factors of 43
List of positive integer factors of 43 that divides 43 without a remainder.
1,43
Factors of 39
List of positive integer factors of 39 that divides 39 without a remainder.
1,3,13,39
Factors of 20
List of positive integer factors of 20 that divides 20 without a remainder.
1,2,4,5,10,20
Greatest Common Factor
We found the factors 43,39,20 . The biggest common factor number is the GCF number.
So the greatest common factor 43,39,20 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 72/43, 84/39, 67/20?
Answer: LCM of Numerators as per given numbers 72/43, 84/39, 67/20 is
LCM of Numerators i.e. for 72,84,67 is 33768
GCF of denominators i.e. for 43,39,20 is 1.
Thus, LCM of Fractions is 33768.Finally, LCM of Fractions for 72/43, 84/39, 67/20 is 33768.