Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 17/66, 33/12, 90/31, 15/624 quickly i.e. 16830 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 17/66, 33/12, 90/31, 15/624 is 16830.
LCM(17/66, 33/12, 90/31, 15/624) = 16830
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 17/66,33/12,90/31,15/624
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 17,33,90,15
Least Common Multiple of Numerators i.e. LCM of 17,33,90,15 is 16830.
GCF of Denominators means GCF of 66,12,31,624 as per the given fractions.
GCF of 66,12,31,624 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 17,33,90,15
3 | 17, 33, 90, 15 |
5 | 17, 11, 30, 5 |
17, 11, 6, 1 |
∴ So the LCM of the given numbers is 3 x 5 x 17 x 11 x 6 x 1 = 16830
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 17,33,90,15 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(17,33,90,15) = 1
common factors(in case of two or more numbers have common factors) = 45
GCF(17,33,90,15) x common factors =1 x 45 = 45
LCM(17,33,90,15) = ( 17 × 33 × 90 × 15 ) / 45
LCM(17,33,90,15) = 757350 / 45
LCM(17,33,90,15) = 16830
Lets's calculate GCF of 66,12,31,624
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 16830/1
Therefore the LCM of Fractions 17/66,33/12,90/31,15/624 is 16830
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 12
List of positive integer factors of 12 that divides 12 without a remainder.
1,2,3,4,6,12
Factors of 31
List of positive integer factors of 31 that divides 31 without a remainder.
1,31
Factors of 624
List of positive integer factors of 624 that divides 624 without a remainder.
1,2,3,4,6,8,12,13,16,24,26,39,48,52,78,104,156,208,312,624
Greatest Common Factor
We found the factors 66,12,31,624 . The biggest common factor number is the GCF number.
So the greatest common factor 66,12,31,624 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 17/66, 33/12, 90/31, 15/624?
Answer: LCM of Numerators as per given numbers 17/66, 33/12, 90/31, 15/624 is
LCM of Numerators i.e. for 17,33,90,15 is 16830
GCF of denominators i.e. for 66,12,31,624 is 1.
Thus, LCM of Fractions is 16830.Finally, LCM of Fractions for 17/66, 33/12, 90/31, 15/624 is 16830.