Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 30/66, 21/40, 76/19, 30/100 quickly i.e. 7980 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 30/66, 21/40, 76/19, 30/100 is 7980.
LCM(30/66, 21/40, 76/19, 30/100) = 7980
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 30/66,21/40,76/19,30/100
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 30,21,76,30
Least Common Multiple of Numerators i.e. LCM of 30,21,76,30 is 7980.
GCF of Denominators means GCF of 66,40,19,100 as per the given fractions.
GCF of 66,40,19,100 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 30,21,76,30
2 | 30, 21, 76, 30 |
3 | 15, 21, 38, 15 |
5 | 5, 7, 38, 5 |
1, 7, 38, 1 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 1 x 7 x 38 x 1 = 7980
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 30,21,76,30 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,21,76,30) = 1
common factors(in case of two or more numbers have common factors) = 180
GCF(30,21,76,30) x common factors =1 x 180 = 180
LCM(30,21,76,30) = ( 30 × 21 × 76 × 30 ) / 180
LCM(30,21,76,30) = 1436400 / 180
LCM(30,21,76,30) = 7980
Lets's calculate GCF of 66,40,19,100
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 7980/1
Therefore the LCM of Fractions 30/66,21/40,76/19,30/100 is 7980
Factors of 66
List of positive integer factors of 66 that divides 66 without a remainder.
1,2,3,6,11,22,33,66
Factors of 40
List of positive integer factors of 40 that divides 40 without a remainder.
1,2,4,5,8,10,20,40
Factors of 19
List of positive integer factors of 19 that divides 19 without a remainder.
1,19
Factors of 100
List of positive integer factors of 100 that divides 100 without a remainder.
1,2,4,5,10,20,25,50,100
Greatest Common Factor
We found the factors 66,40,19,100 . The biggest common factor number is the GCF number.
So the greatest common factor 66,40,19,100 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 30/66, 21/40, 76/19, 30/100?
Answer: LCM of Numerators as per given numbers 30/66, 21/40, 76/19, 30/100 is
LCM of Numerators i.e. for 30,21,76,30 is 7980
GCF of denominators i.e. for 66,40,19,100 is 1.
Thus, LCM of Fractions is 7980.Finally, LCM of Fractions for 30/66, 21/40, 76/19, 30/100 is 7980.