Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 12/89, 42/20, 420/840 quickly i.e. 420 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 12/89, 42/20, 420/840 is 420.
LCM(12/89, 42/20, 420/840) = 420
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 12/89,42/20,420/840
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 12,42,420
Least Common Multiple of Numerators i.e. LCM of 12,42,420 is 420.
GCF of Denominators means GCF of 89,20,840 as per the given fractions.
GCF of 89,20,840 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 12,42,420
2 | 12, 42, 420 |
2 | 6, 21, 210 |
3 | 3, 21, 105 |
7 | 1, 7, 35 |
1, 1, 5 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 7 x 1 x 1 x 5 = 420
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 12,42,420 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(12,42,420) = 6
common factors(in case of two or more numbers have common factors) = 84
GCF(12,42,420) x common factors =6 x 84 = 504
LCM(12,42,420) = ( 12 × 42 × 420 ) / 504
LCM(12,42,420) = 211680 / 504
LCM(12,42,420) = 420
Lets's calculate GCF of 89,20,840
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 420/1
Therefore the LCM of Fractions 12/89,42/20,420/840 is 420
Factors of 89
List of positive integer factors of 89 that divides 89 without a remainder.
1,89
Factors of 20
List of positive integer factors of 20 that divides 20 without a remainder.
1,2,4,5,10,20
Factors of 840
List of positive integer factors of 840 that divides 840 without a remainder.
1,2,3,4,5,6,7,8,10,12,14,15,20,21,24,28,30,35,40,42,56,60,70,84,105,120,140,168,210,280,420,840
Greatest Common Factor
We found the factors 89,20,840 . The biggest common factor number is the GCF number.
So the greatest common factor 89,20,840 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 12/89, 42/20, 420/840?
Answer: LCM of Numerators as per given numbers 12/89, 42/20, 420/840 is
LCM of Numerators i.e. for 12,42,420 is 420
GCF of denominators i.e. for 89,20,840 is 1.
Thus, LCM of Fractions is 420.Finally, LCM of Fractions for 12/89, 42/20, 420/840 is 420.