Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 748/172, 828/612, 414/330 quickly i.e. 77418 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 748/172, 828/612, 414/330 is 77418.
LCM(748/172, 828/612, 414/330) = 77418
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 748/172,828/612,414/330
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 748,828,414
Least Common Multiple of Numerators i.e. LCM of 748,828,414 is 154836.
GCF of Denominators means GCF of 172,612,330 as per the given fractions.
GCF of 172,612,330 is 2 as it is the largest common factor for these numbers.
Lets's calculate LCM of 748,828,414
2 | 748, 828, 414 |
2 | 374, 414, 207 |
3 | 187, 207, 207 |
3 | 187, 69, 69 |
23 | 187, 23, 23 |
187, 1, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 23 x 187 x 1 x 1 = 154836
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 748,828,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(748,828,414) = 2
common factors(in case of two or more numbers have common factors) = 828
GCF(748,828,414) x common factors =2 x 828 = 1656
LCM(748,828,414) = ( 748 × 828 × 414 ) / 1656
LCM(748,828,414) = 256408416 / 1656
LCM(748,828,414) = 154836
Lets's calculate GCF of 172,612,330
2 | 172, 612, 330 |
86, 306, 165 |
∴ So the GCF of the given numbers is 2 = 2
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 154836/2
Therefore the LCM of Fractions 748/172,828/612,414/330 is 77418
Factors of 172
List of positive integer factors of 172 that divides 172 without a remainder.
1,2,4,43,86,172
Factors of 612
List of positive integer factors of 612 that divides 612 without a remainder.
1,2,3,4,6,9,12,17,18,34,36,51,68,102,153,204,306,612
Factors of 330
List of positive integer factors of 330 that divides 330 without a remainder.
1,2,3,5,6,10,11,15,22,30,33,55,66,110,165,330
Greatest Common Factor
We found the factors 172,612,330 . The biggest common factor number is the GCF number.
So the greatest common factor 172,612,330 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 748/172, 828/612, 414/330?
Answer: LCM of Numerators as per given numbers 748/172, 828/612, 414/330 is
LCM of Numerators i.e. for 748,828,414 is 154836
GCF of denominators i.e. for 172,612,330 is 2.
Thus, LCM of Fractions is 77418.Finally, LCM of Fractions for 748/172, 828/612, 414/330 is 77418.