Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 6/46, 78/27, 21/71 quickly i.e. 546 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 6/46, 78/27, 21/71 is 546.
LCM(6/46, 78/27, 21/71) = 546
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 6/46,78/27,21/71
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 6,78,21
Least Common Multiple of Numerators i.e. LCM of 6,78,21 is 546.
GCF of Denominators means GCF of 46,27,71 as per the given fractions.
GCF of 46,27,71 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 6,78,21
2 | 6, 78, 21 |
3 | 3, 39, 21 |
1, 13, 7 |
∴ So the LCM of the given numbers is 2 x 3 x 1 x 13 x 7 = 546
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 6,78,21 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(6,78,21) = 3
common factors(in case of two or more numbers have common factors) = 6
GCF(6,78,21) x common factors =3 x 6 = 18
LCM(6,78,21) = ( 6 × 78 × 21 ) / 18
LCM(6,78,21) = 9828 / 18
LCM(6,78,21) = 546
Lets's calculate GCF of 46,27,71
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 546/1
Therefore the LCM of Fractions 6/46,78/27,21/71 is 546
Factors of 46
List of positive integer factors of 46 that divides 46 without a remainder.
1,2,23,46
Factors of 27
List of positive integer factors of 27 that divides 27 without a remainder.
1,3,9,27
Factors of 71
List of positive integer factors of 71 that divides 71 without a remainder.
1,71
Greatest Common Factor
We found the factors 46,27,71 . The biggest common factor number is the GCF number.
So the greatest common factor 46,27,71 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 6/46, 78/27, 21/71?
Answer: LCM of Numerators as per given numbers 6/46, 78/27, 21/71 is
LCM of Numerators i.e. for 6,78,21 is 546
GCF of denominators i.e. for 46,27,71 is 1.
Thus, LCM of Fractions is 546.Finally, LCM of Fractions for 6/46, 78/27, 21/71 is 546.