Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 75/36, 240/83, 360/735 quickly i.e. 3600 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 75/36, 240/83, 360/735 is 3600.
LCM(75/36, 240/83, 360/735) = 3600
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 75/36,240/83,360/735
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 75,240,360
Least Common Multiple of Numerators i.e. LCM of 75,240,360 is 3600.
GCF of Denominators means GCF of 36,83,735 as per the given fractions.
GCF of 36,83,735 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 75,240,360
2 | 75, 240, 360 |
2 | 75, 120, 180 |
2 | 75, 60, 90 |
3 | 75, 30, 45 |
5 | 25, 10, 15 |
5, 2, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 5 x 5 x 2 x 3 = 3600
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 75,240,360 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,240,360) = 15
common factors(in case of two or more numbers have common factors) = 120
GCF(75,240,360) x common factors =15 x 120 = 1800
LCM(75,240,360) = ( 75 × 240 × 360 ) / 1800
LCM(75,240,360) = 6480000 / 1800
LCM(75,240,360) = 3600
Lets's calculate GCF of 36,83,735
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 3600/1
Therefore the LCM of Fractions 75/36,240/83,360/735 is 3600
Factors of 36
List of positive integer factors of 36 that divides 36 without a remainder.
1,2,3,4,6,9,12,18,36
Factors of 83
List of positive integer factors of 83 that divides 83 without a remainder.
1,83
Factors of 735
List of positive integer factors of 735 that divides 735 without a remainder.
1,3,5,7,15,21,35,49,105,147,245,735
Greatest Common Factor
We found the factors 36,83,735 . The biggest common factor number is the GCF number.
So the greatest common factor 36,83,735 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 75/36, 240/83, 360/735?
Answer: LCM of Numerators as per given numbers 75/36, 240/83, 360/735 is
LCM of Numerators i.e. for 75,240,360 is 3600
GCF of denominators i.e. for 36,83,735 is 1.
Thus, LCM of Fractions is 3600.Finally, LCM of Fractions for 75/36, 240/83, 360/735 is 3600.