Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 76/67, 16/83, 10/18, 32/460 quickly i.e. 3040 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 76/67, 16/83, 10/18, 32/460 is 3040.
LCM(76/67, 16/83, 10/18, 32/460) = 3040
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 76/67,16/83,10/18,32/460
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 76,16,10,32
Least Common Multiple of Numerators i.e. LCM of 76,16,10,32 is 3040.
GCF of Denominators means GCF of 67,83,18,460 as per the given fractions.
GCF of 67,83,18,460 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 76,16,10,32
2 | 76, 16, 10, 32 |
2 | 38, 8, 5, 16 |
2 | 19, 4, 5, 8 |
2 | 19, 2, 5, 4 |
19, 1, 5, 2 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 19 x 1 x 5 x 2 = 3040
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 76,16,10,32 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(76,16,10,32) = 2
common factors(in case of two or more numbers have common factors) = 64
GCF(76,16,10,32) x common factors =2 x 64 = 128
LCM(76,16,10,32) = ( 76 × 16 × 10 × 32 ) / 128
LCM(76,16,10,32) = 389120 / 128
LCM(76,16,10,32) = 3040
Lets's calculate GCF of 67,83,18,460
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 3040/1
Therefore the LCM of Fractions 76/67,16/83,10/18,32/460 is 3040
Factors of 67
List of positive integer factors of 67 that divides 67 without a remainder.
1,67
Factors of 83
List of positive integer factors of 83 that divides 83 without a remainder.
1,83
Factors of 18
List of positive integer factors of 18 that divides 18 without a remainder.
1,2,3,6,9,18
Factors of 460
List of positive integer factors of 460 that divides 460 without a remainder.
1,2,4,5,10,20,23,46,92,115,230,460
Greatest Common Factor
We found the factors 67,83,18,460 . The biggest common factor number is the GCF number.
So the greatest common factor 67,83,18,460 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 76/67, 16/83, 10/18, 32/460?
Answer: LCM of Numerators as per given numbers 76/67, 16/83, 10/18, 32/460 is
LCM of Numerators i.e. for 76,16,10,32 is 3040
GCF of denominators i.e. for 67,83,18,460 is 1.
Thus, LCM of Fractions is 3040.Finally, LCM of Fractions for 76/67, 16/83, 10/18, 32/460 is 3040.