Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 5/35, 7/30, 40/62, 99/420 quickly i.e. 27720 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 5/35, 7/30, 40/62, 99/420 is 27720.
LCM(5/35, 7/30, 40/62, 99/420) = 27720
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 5/35,7/30,40/62,99/420
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 5,7,40,99
Least Common Multiple of Numerators i.e. LCM of 5,7,40,99 is 27720.
GCF of Denominators means GCF of 35,30,62,420 as per the given fractions.
GCF of 35,30,62,420 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 5,7,40,99
5 | 5, 7, 40, 99 |
1, 7, 8, 99 |
∴ So the LCM of the given numbers is 5 x 1 x 7 x 8 x 99 = 27720
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 5,7,40,99 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(5,7,40,99) = 1
common factors(in case of two or more numbers have common factors) = 5
GCF(5,7,40,99) x common factors =1 x 5 = 5
LCM(5,7,40,99) = ( 5 × 7 × 40 × 99 ) / 5
LCM(5,7,40,99) = 138600 / 5
LCM(5,7,40,99) = 27720
Lets's calculate GCF of 35,30,62,420
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 27720/1
Therefore the LCM of Fractions 5/35,7/30,40/62,99/420 is 27720
Factors of 35
List of positive integer factors of 35 that divides 35 without a remainder.
1,5,7,35
Factors of 30
List of positive integer factors of 30 that divides 30 without a remainder.
1,2,3,5,6,10,15,30
Factors of 62
List of positive integer factors of 62 that divides 62 without a remainder.
1,2,31,62
Factors of 420
List of positive integer factors of 420 that divides 420 without a remainder.
1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 35,30,62,420 . The biggest common factor number is the GCF number.
So the greatest common factor 35,30,62,420 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 5/35, 7/30, 40/62, 99/420?
Answer: LCM of Numerators as per given numbers 5/35, 7/30, 40/62, 99/420 is
LCM of Numerators i.e. for 5,7,40,99 is 27720
GCF of denominators i.e. for 35,30,62,420 is 1.
Thus, LCM of Fractions is 27720.Finally, LCM of Fractions for 5/35, 7/30, 40/62, 99/420 is 27720.