Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 42/69, 75/12, 783/165 quickly i.e. 91350 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 42/69, 75/12, 783/165 is 91350.
LCM(42/69, 75/12, 783/165) = 91350
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 42/69,75/12,783/165
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 42,75,783
Least Common Multiple of Numerators i.e. LCM of 42,75,783 is 274050.
GCF of Denominators means GCF of 69,12,165 as per the given fractions.
GCF of 69,12,165 is 3 as it is the largest common factor for these numbers.
Lets's calculate LCM of 42,75,783
3 | 42, 75, 783 |
14, 25, 261 |
∴ So the LCM of the given numbers is 3 x 14 x 25 x 261 = 274050
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 42,75,783 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,75,783) = 3
common factors(in case of two or more numbers have common factors) = 3
GCF(42,75,783) x common factors =3 x 3 = 9
LCM(42,75,783) = ( 42 × 75 × 783 ) / 9
LCM(42,75,783) = 2466450 / 9
LCM(42,75,783) = 274050
Lets's calculate GCF of 69,12,165
3 | 69, 12, 165 |
23, 4, 55 |
∴ So the GCF of the given numbers is 3 = 3
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 274050/3
Therefore the LCM of Fractions 42/69,75/12,783/165 is 91350
Factors of 69
List of positive integer factors of 69 that divides 69 without a remainder.
1,3,23,69
Factors of 12
List of positive integer factors of 12 that divides 12 without a remainder.
1,2,3,4,6,12
Factors of 165
List of positive integer factors of 165 that divides 165 without a remainder.
1,3,5,11,15,33,55,165
Greatest Common Factor
We found the factors 69,12,165 . The biggest common factor number is the GCF number.
So the greatest common factor 69,12,165 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 42/69, 75/12, 783/165?
Answer: LCM of Numerators as per given numbers 42/69, 75/12, 783/165 is
LCM of Numerators i.e. for 42,75,783 is 274050
GCF of denominators i.e. for 69,12,165 is 3.
Thus, LCM of Fractions is 91350.Finally, LCM of Fractions for 42/69, 75/12, 783/165 is 91350.