Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 37/34, 32/72, 312/24 quickly i.e. 23088 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 37/34, 32/72, 312/24 is 23088.
LCM(37/34, 32/72, 312/24) = 23088
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 37/34,32/72,312/24
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 37,32,312
Least Common Multiple of Numerators i.e. LCM of 37,32,312 is 46176.
GCF of Denominators means GCF of 34,72,24 as per the given fractions.
GCF of 34,72,24 is 2 as it is the largest common factor for these numbers.
Lets's calculate LCM of 37,32,312
2 | 37, 32, 312 |
2 | 37, 16, 156 |
2 | 37, 8, 78 |
37, 4, 39 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 37 x 4 x 39 = 46176
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 37,32,312 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(37,32,312) = 1
common factors(in case of two or more numbers have common factors) = 8
GCF(37,32,312) x common factors =1 x 8 = 8
LCM(37,32,312) = ( 37 × 32 × 312 ) / 8
LCM(37,32,312) = 369408 / 8
LCM(37,32,312) = 46176
Lets's calculate GCF of 34,72,24
2 | 34, 72, 24 |
17, 36, 12 |
∴ So the GCF of the given numbers is 2 = 2
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 46176/2
Therefore the LCM of Fractions 37/34,32/72,312/24 is 23088
Factors of 34
List of positive integer factors of 34 that divides 34 without a remainder.
1,2,17,34
Factors of 72
List of positive integer factors of 72 that divides 72 without a remainder.
1,2,3,4,6,8,9,12,18,24,36,72
Factors of 24
List of positive integer factors of 24 that divides 24 without a remainder.
1,2,3,4,6,8,12,24
Greatest Common Factor
We found the factors 34,72,24 . The biggest common factor number is the GCF number.
So the greatest common factor 34,72,24 is 2.
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 37/34, 32/72, 312/24?
Answer: LCM of Numerators as per given numbers 37/34, 32/72, 312/24 is
LCM of Numerators i.e. for 37,32,312 is 46176
GCF of denominators i.e. for 34,72,24 is 2.
Thus, LCM of Fractions is 23088.Finally, LCM of Fractions for 37/34, 32/72, 312/24 is 23088.