Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 31/66, 35/87, 32/51, 51/159 quickly i.e. 590240 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 31/66, 35/87, 32/51, 51/159 is 590240.
LCM(31/66, 35/87, 32/51, 51/159) = 590240
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 31/66,35/87,32/51,51/159
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 31,35,32,51
Least Common Multiple of Numerators i.e. LCM of 31,35,32,51 is 1770720.
GCF of Denominators means GCF of 66,87,51,159 as per the given fractions.
GCF of 66,87,51,159 is 3 as it is the largest common factor for these numbers.
Lets's calculate LCM of 31,35,32,51
Given numbers has no common factors except 1. So, there LCM is their product i.e 1770720
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 31,35,32,51 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,35,32,51) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(31,35,32,51) x common factors =1 x 1 = 1
LCM(31,35,32,51) = ( 31 × 35 × 32 × 51 ) / 1
LCM(31,35,32,51) = 1770720 / 1
LCM(31,35,32,51) = 1770720
Lets's calculate GCF of 66,87,51,159
3 | 66, 87, 51, 159 |
22, 29, 17, 53 |
∴ So the GCF of the given numbers is 3 = 3
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 1770720/3
Therefore the LCM of Fractions 31/66,35/87,32/51,51/159 is 590240
Factors of 66
List of positive integer factors of 66 that divides 66 without a remainder.
1,2,3,6,11,22,33,66
Factors of 87
List of positive integer factors of 87 that divides 87 without a remainder.
1,3,29,87
Factors of 51
List of positive integer factors of 51 that divides 51 without a remainder.
1,3,17,51
Factors of 159
List of positive integer factors of 159 that divides 159 without a remainder.
1,3,53,159
Greatest Common Factor
We found the factors 66,87,51,159 . The biggest common factor number is the GCF number.
So the greatest common factor 66,87,51,159 is 3.
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 31/66, 35/87, 32/51, 51/159?
Answer: LCM of Numerators as per given numbers 31/66, 35/87, 32/51, 51/159 is
LCM of Numerators i.e. for 31,35,32,51 is 1770720
GCF of denominators i.e. for 66,87,51,159 is 3.
Thus, LCM of Fractions is 590240.Finally, LCM of Fractions for 31/66, 35/87, 32/51, 51/159 is 590240.