Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 66/40, 49/21, 31/86, 91/140 quickly i.e. 1303302 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 66/40, 49/21, 31/86, 91/140 is 1303302.
LCM(66/40, 49/21, 31/86, 91/140) = 1303302
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 66/40,49/21,31/86,91/140
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 66,49,31,91
Least Common Multiple of Numerators i.e. LCM of 66,49,31,91 is 1303302.
GCF of Denominators means GCF of 40,21,86,140 as per the given fractions.
GCF of 40,21,86,140 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 66,49,31,91
7 | 66, 49, 31, 91 |
66, 7, 31, 13 |
∴ So the LCM of the given numbers is 7 x 66 x 7 x 31 x 13 = 1303302
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 66,49,31,91 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(66,49,31,91) = 1
common factors(in case of two or more numbers have common factors) = 7
GCF(66,49,31,91) x common factors =1 x 7 = 7
LCM(66,49,31,91) = ( 66 × 49 × 31 × 91 ) / 7
LCM(66,49,31,91) = 9123114 / 7
LCM(66,49,31,91) = 1303302
Lets's calculate GCF of 40,21,86,140
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 1303302/1
Therefore the LCM of Fractions 66/40,49/21,31/86,91/140 is 1303302
Factors of 40
List of positive integer factors of 40 that divides 40 without a remainder.
1,2,4,5,8,10,20,40
Factors of 21
List of positive integer factors of 21 that divides 21 without a remainder.
1,3,7,21
Factors of 86
List of positive integer factors of 86 that divides 86 without a remainder.
1,2,43,86
Factors of 140
List of positive integer factors of 140 that divides 140 without a remainder.
1,2,4,5,7,10,14,20,28,35,70,140
Greatest Common Factor
We found the factors 40,21,86,140 . The biggest common factor number is the GCF number.
So the greatest common factor 40,21,86,140 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 66/40, 49/21, 31/86, 91/140?
Answer: LCM of Numerators as per given numbers 66/40, 49/21, 31/86, 91/140 is
LCM of Numerators i.e. for 66,49,31,91 is 1303302
GCF of denominators i.e. for 40,21,86,140 is 1.
Thus, LCM of Fractions is 1303302.Finally, LCM of Fractions for 66/40, 49/21, 31/86, 91/140 is 1303302.