Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 45/53, 14/75, 21/46, 84/32 quickly i.e. 1260 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 45/53, 14/75, 21/46, 84/32 is 1260.
LCM(45/53, 14/75, 21/46, 84/32) = 1260
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 45/53,14/75,21/46,84/32
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 45,14,21,84
Least Common Multiple of Numerators i.e. LCM of 45,14,21,84 is 1260.
GCF of Denominators means GCF of 53,75,46,32 as per the given fractions.
GCF of 53,75,46,32 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 45,14,21,84
2 | 45, 14, 21, 84 |
3 | 45, 7, 21, 42 |
7 | 15, 7, 7, 14 |
15, 1, 1, 2 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 15 x 1 x 1 x 2 = 1260
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 45,14,21,84 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(45,14,21,84) = 1
common factors(in case of two or more numbers have common factors) = 882
GCF(45,14,21,84) x common factors =1 x 882 = 882
LCM(45,14,21,84) = ( 45 × 14 × 21 × 84 ) / 882
LCM(45,14,21,84) = 1111320 / 882
LCM(45,14,21,84) = 1260
Lets's calculate GCF of 53,75,46,32
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 1260/1
Therefore the LCM of Fractions 45/53,14/75,21/46,84/32 is 1260
Factors of 53
List of positive integer factors of 53 that divides 53 without a remainder.
1,53
Factors of 75
List of positive integer factors of 75 that divides 75 without a remainder.
1,3,5,15,25,75
Factors of 46
List of positive integer factors of 46 that divides 46 without a remainder.
1,2,23,46
Factors of 32
List of positive integer factors of 32 that divides 32 without a remainder.
1,2,4,8,16,32
Greatest Common Factor
We found the factors 53,75,46,32 . The biggest common factor number is the GCF number.
So the greatest common factor 53,75,46,32 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 45/53, 14/75, 21/46, 84/32?
Answer: LCM of Numerators as per given numbers 45/53, 14/75, 21/46, 84/32 is
LCM of Numerators i.e. for 45,14,21,84 is 1260
GCF of denominators i.e. for 53,75,46,32 is 1.
Thus, LCM of Fractions is 1260.Finally, LCM of Fractions for 45/53, 14/75, 21/46, 84/32 is 1260.