Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 16/70, 78/70, 31/875 quickly i.e. 19344/35 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 16/70, 78/70, 31/875 is 19344/35.
LCM(16/70, 78/70, 31/875) = 19344/35
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 16/70,78/70,31/875
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 16,78,31
Least Common Multiple of Numerators i.e. LCM of 16,78,31 is 19344.
GCF of Denominators means GCF of 70,70,875 as per the given fractions.
GCF of 70,70,875 is 35 as it is the largest common factor for these numbers.
Lets's calculate LCM of 16,78,31
2 | 16, 78, 31 |
8, 39, 31 |
∴ So the LCM of the given numbers is 2 x 8 x 39 x 31 = 19344
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 16,78,31 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(16,78,31) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(16,78,31) x common factors =1 x 2 = 2
LCM(16,78,31) = ( 16 × 78 × 31 ) / 2
LCM(16,78,31) = 38688 / 2
LCM(16,78,31) = 19344
Lets's calculate GCF of 70,70,875
5 | 70, 70, 875 |
7 | 14, 14, 175 |
2, 2, 25 |
∴ So the GCF of the given numbers is 5 x 7 = 35
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 19344/35
Therefore the LCM of Fractions 16/70,78/70,31/875 is 19344/35
Factors of 70
List of positive integer factors of 70 that divides 70 without a remainder.
1,2,5,7,10,14,35,70
Factors of 70
List of positive integer factors of 70 that divides 70 without a remainder.
1,2,5,7,10,14,35,70
Factors of 875
List of positive integer factors of 875 that divides 875 without a remainder.
1,5,7,25,35,125,175,875
Greatest Common Factor
We found the factors 70,70,875 . The biggest common factor number is the GCF number.
So the greatest common factor 70,70,875 is 35.
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 16/70, 78/70, 31/875?
Answer: LCM of Numerators as per given numbers 16/70, 78/70, 31/875 is
LCM of Numerators i.e. for 16,78,31 is 19344
GCF of denominators i.e. for 70,70,875 is 35.
Thus, LCM of Fractions is 19344/35.Finally, LCM of Fractions for 16/70, 78/70, 31/875 is 19344/35.