Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 32/42, 23/76, 278/11 quickly i.e. 102304 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 32/42, 23/76, 278/11 is 102304.
LCM(32/42, 23/76, 278/11) = 102304
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 32/42,23/76,278/11
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 32,23,278
Least Common Multiple of Numerators i.e. LCM of 32,23,278 is 102304.
GCF of Denominators means GCF of 42,76,11 as per the given fractions.
GCF of 42,76,11 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 32,23,278
2 | 32, 23, 278 |
16, 23, 139 |
∴ So the LCM of the given numbers is 2 x 16 x 23 x 139 = 102304
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 32,23,278 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,23,278) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(32,23,278) x common factors =1 x 2 = 2
LCM(32,23,278) = ( 32 × 23 × 278 ) / 2
LCM(32,23,278) = 204608 / 2
LCM(32,23,278) = 102304
Lets's calculate GCF of 42,76,11
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 102304/1
Therefore the LCM of Fractions 32/42,23/76,278/11 is 102304
Factors of 42
List of positive integer factors of 42 that divides 42 without a remainder.
1,2,3,6,7,14,21,42
Factors of 76
List of positive integer factors of 76 that divides 76 without a remainder.
1,2,4,19,38,76
Factors of 11
List of positive integer factors of 11 that divides 11 without a remainder.
1,11
Greatest Common Factor
We found the factors 42,76,11 . The biggest common factor number is the GCF number.
So the greatest common factor 42,76,11 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 32/42, 23/76, 278/11?
Answer: LCM of Numerators as per given numbers 32/42, 23/76, 278/11 is
LCM of Numerators i.e. for 32,23,278 is 102304
GCF of denominators i.e. for 42,76,11 is 1.
Thus, LCM of Fractions is 102304.Finally, LCM of Fractions for 32/42, 23/76, 278/11 is 102304.