Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 32/71, 488/34, 214/175 quickly i.e. 208864 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 32/71, 488/34, 214/175 is 208864.
LCM(32/71, 488/34, 214/175) = 208864
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 32/71,488/34,214/175
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 32,488,214
Least Common Multiple of Numerators i.e. LCM of 32,488,214 is 208864.
GCF of Denominators means GCF of 71,34,175 as per the given fractions.
GCF of 71,34,175 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 32,488,214
2 | 32, 488, 214 |
2 | 16, 244, 107 |
2 | 8, 122, 107 |
4, 61, 107 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 4 x 61 x 107 = 208864
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 32,488,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,488,214) = 2
common factors(in case of two or more numbers have common factors) = 8
GCF(32,488,214) x common factors =2 x 8 = 16
LCM(32,488,214) = ( 32 × 488 × 214 ) / 16
LCM(32,488,214) = 3341824 / 16
LCM(32,488,214) = 208864
Lets's calculate GCF of 71,34,175
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 208864/1
Therefore the LCM of Fractions 32/71,488/34,214/175 is 208864
Factors of 71
List of positive integer factors of 71 that divides 71 without a remainder.
1,71
Factors of 34
List of positive integer factors of 34 that divides 34 without a remainder.
1,2,17,34
Factors of 175
List of positive integer factors of 175 that divides 175 without a remainder.
1,5,7,25,35,175
Greatest Common Factor
We found the factors 71,34,175 . The biggest common factor number is the GCF number.
So the greatest common factor 71,34,175 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 32/71, 488/34, 214/175?
Answer: LCM of Numerators as per given numbers 32/71, 488/34, 214/175 is
LCM of Numerators i.e. for 32,488,214 is 208864
GCF of denominators i.e. for 71,34,175 is 1.
Thus, LCM of Fractions is 208864.Finally, LCM of Fractions for 32/71, 488/34, 214/175 is 208864.