Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 72/40, 30/98, 64/56, 90/349 quickly i.e. 2880 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 72/40, 30/98, 64/56, 90/349 is 2880.
LCM(72/40, 30/98, 64/56, 90/349) = 2880
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 72/40,30/98,64/56,90/349
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 72,30,64,90
Least Common Multiple of Numerators i.e. LCM of 72,30,64,90 is 2880.
GCF of Denominators means GCF of 40,98,56,349 as per the given fractions.
GCF of 40,98,56,349 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 72,30,64,90
2 | 72, 30, 64, 90 |
2 | 36, 15, 32, 45 |
2 | 18, 15, 16, 45 |
3 | 9, 15, 8, 45 |
3 | 3, 5, 8, 15 |
5 | 1, 5, 8, 5 |
1, 1, 8, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 3 x 5 x 1 x 1 x 8 x 1 = 2880
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 72,30,64,90 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(72,30,64,90) = 2
common factors(in case of two or more numbers have common factors) = 2160
GCF(72,30,64,90) x common factors =2 x 2160 = 4320
LCM(72,30,64,90) = ( 72 × 30 × 64 × 90 ) / 4320
LCM(72,30,64,90) = 12441600 / 4320
LCM(72,30,64,90) = 2880
Lets's calculate GCF of 40,98,56,349
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 2880/1
Therefore the LCM of Fractions 72/40,30/98,64/56,90/349 is 2880
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 98
List of positive integer factors of 98 that divides 98 without a remainder.
1,2,7,14,49,98
Factors of 56
List of positive integer factors of 56 that divides 56 without a remainder.
1,2,4,7,8,14,28,56
Factors of 349
List of positive integer factors of 349 that divides 349 without a remainder.
1,349
Greatest Common Factor
We found the factors 40,98,56,349 . The biggest common factor number is the GCF number.
So the greatest common factor 40,98,56,349 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 72/40, 30/98, 64/56, 90/349?
Answer: LCM of Numerators as per given numbers 72/40, 30/98, 64/56, 90/349 is
LCM of Numerators i.e. for 72,30,64,90 is 2880
GCF of denominators i.e. for 40,98,56,349 is 1.
Thus, LCM of Fractions is 2880.Finally, LCM of Fractions for 72/40, 30/98, 64/56, 90/349 is 2880.