Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 360/462, 915/702, 540/189 quickly i.e. 21960 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 360/462, 915/702, 540/189 is 21960.
LCM(360/462, 915/702, 540/189) = 21960
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 360/462,915/702,540/189
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 360,915,540
Least Common Multiple of Numerators i.e. LCM of 360,915,540 is 65880.
GCF of Denominators means GCF of 462,702,189 as per the given fractions.
GCF of 462,702,189 is 3 as it is the largest common factor for these numbers.
Lets's calculate LCM of 360,915,540
2 | 360, 915, 540 |
2 | 180, 915, 270 |
3 | 90, 915, 135 |
3 | 30, 305, 45 |
5 | 10, 305, 15 |
2, 61, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 5 x 2 x 61 x 3 = 65880
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 360,915,540 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(360,915,540) = 15
common factors(in case of two or more numbers have common factors) = 180
GCF(360,915,540) x common factors =15 x 180 = 2700
LCM(360,915,540) = ( 360 × 915 × 540 ) / 2700
LCM(360,915,540) = 177876000 / 2700
LCM(360,915,540) = 65880
Lets's calculate GCF of 462,702,189
3 | 462, 702, 189 |
154, 234, 63 |
∴ So the GCF of the given numbers is 3 = 3
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 65880/3
Therefore the LCM of Fractions 360/462,915/702,540/189 is 21960
Factors of 462
List of positive integer factors of 462 that divides 462 without a remainder.
1,2,3,6,7,11,14,21,22,33,42,66,77,154,231,462
Factors of 702
List of positive integer factors of 702 that divides 702 without a remainder.
1,2,3,6,9,13,18,26,27,39,54,78,117,234,351,702
Factors of 189
List of positive integer factors of 189 that divides 189 without a remainder.
1,3,7,9,21,27,63,189
Greatest Common Factor
We found the factors 462,702,189 . The biggest common factor number is the GCF number.
So the greatest common factor 462,702,189 is 3.
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 360/462, 915/702, 540/189?
Answer: LCM of Numerators as per given numbers 360/462, 915/702, 540/189 is
LCM of Numerators i.e. for 360,915,540 is 65880
GCF of denominators i.e. for 462,702,189 is 3.
Thus, LCM of Fractions is 21960.Finally, LCM of Fractions for 360/462, 915/702, 540/189 is 21960.