Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 75/222, 70/200, 189/996 quickly i.e. 4725 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 75/222, 70/200, 189/996 is 4725.
LCM(75/222, 70/200, 189/996) = 4725
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 75/222,70/200,189/996
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 75,70,189
Least Common Multiple of Numerators i.e. LCM of 75,70,189 is 9450.
GCF of Denominators means GCF of 222,200,996 as per the given fractions.
GCF of 222,200,996 is 2 as it is the largest common factor for these numbers.
Lets's calculate LCM of 75,70,189
3 | 75, 70, 189 |
5 | 25, 70, 63 |
7 | 5, 14, 63 |
5, 2, 9 |
∴ So the LCM of the given numbers is 3 x 5 x 7 x 5 x 2 x 9 = 9450
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 75,70,189 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,70,189) = 1
common factors(in case of two or more numbers have common factors) = 105
GCF(75,70,189) x common factors =1 x 105 = 105
LCM(75,70,189) = ( 75 × 70 × 189 ) / 105
LCM(75,70,189) = 992250 / 105
LCM(75,70,189) = 9450
Lets's calculate GCF of 222,200,996
2 | 222, 200, 996 |
111, 100, 498 |
∴ So the GCF of the given numbers is 2 = 2
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 9450/2
Therefore the LCM of Fractions 75/222,70/200,189/996 is 4725
Factors of 222
List of positive integer factors of 222 that divides 222 without a remainder.
1,2,3,6,37,74,111,222
Factors of 200
List of positive integer factors of 200 that divides 200 without a remainder.
1,2,4,5,8,10,20,25,40,50,100,200
Factors of 996
List of positive integer factors of 996 that divides 996 without a remainder.
1,2,3,4,6,12,83,166,249,332,498,996
Greatest Common Factor
We found the factors 222,200,996 . The biggest common factor number is the GCF number.
So the greatest common factor 222,200,996 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 75/222, 70/200, 189/996?
Answer: LCM of Numerators as per given numbers 75/222, 70/200, 189/996 is
LCM of Numerators i.e. for 75,70,189 is 9450
GCF of denominators i.e. for 222,200,996 is 2.
Thus, LCM of Fractions is 4725.Finally, LCM of Fractions for 75/222, 70/200, 189/996 is 4725.