Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 68/342, 30/438 quickly i.e. 170 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 68/342, 30/438 is 170.
LCM(68/342, 30/438) = 170
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 68/342,30/438
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 68,30
Least Common Multiple of Numerators i.e. LCM of 68,30 is 1020.
GCF of Denominators means GCF of 342,438 as per the given fractions.
GCF of 342,438 is 6 as it is the largest common factor for these numbers.
Lets's calculate LCM of 68,30
2 | 68, 30 |
34, 15 |
∴ So the LCM of the given numbers is 2 x 34 x 15 = 1020
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 68,30 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(68,30) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(68,30) x common factors =2 x 1 = 2
LCM(68,30) = ( 68 × 30 ) / 2
LCM(68,30) = 2040 / 2
LCM(68,30) = 1020
Lets's calculate GCF of 342,438
2 | 342, 438 |
3 | 171, 219 |
57, 73 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 1020/6
Therefore the LCM of Fractions 68/342,30/438 is 170
Factors of 342
List of positive integer factors of 342 that divides 342 without a remainder.
1,2,3,6,9,18,19,38,57,114,171,342
Factors of 438
List of positive integer factors of 438 that divides 438 without a remainder.
1,2,3,6,73,146,219,438
Greatest Common Factor
We found the factors 342,438 . The biggest common factor number is the GCF number.
So the greatest common factor 342,438 is 6.
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 68/342, 30/438?
Answer: LCM of Numerators as per given numbers 68/342, 30/438 is
LCM of Numerators i.e. for 68,30 is 1020
GCF of denominators i.e. for 342,438 is 6.
Thus, LCM of Fractions is 170.Finally, LCM of Fractions for 68/342, 30/438 is 170.