Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 7/48, 1/72, 75/84, 14/300 quickly i.e. 1050/12 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 7/48, 1/72, 75/84, 14/300 is 1050/12.
LCM(7/48, 1/72, 75/84, 14/300) = 1050/12
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 7/48,1/72,75/84,14/300
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 7,1,75,14
Least Common Multiple of Numerators i.e. LCM of 7,1,75,14 is 1050.
GCF of Denominators means GCF of 48,72,84,300 as per the given fractions.
GCF of 48,72,84,300 is 12 as it is the largest common factor for these numbers.
Lets's calculate LCM of 7,1,75,14
7 | 7, 1, 75, 14 |
1, 1, 75, 2 |
∴ So the LCM of the given numbers is 7 x 1 x 1 x 75 x 2 = 1050
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 7,1,75,14 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(7,1,75,14) = 1
common factors(in case of two or more numbers have common factors) = 7
GCF(7,1,75,14) x common factors =1 x 7 = 7
LCM(7,1,75,14) = ( 7 × 1 × 75 × 14 ) / 7
LCM(7,1,75,14) = 7350 / 7
LCM(7,1,75,14) = 1050
Lets's calculate GCF of 48,72,84,300
2 | 48, 72, 84, 300 |
2 | 24, 36, 42, 150 |
3 | 12, 18, 21, 75 |
4, 6, 7, 25 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 1050/12
Therefore the LCM of Fractions 7/48,1/72,75/84,14/300 is 1050/12
Factors of 48
List of positive integer factors of 48 that divides 48 without a remainder.
1,2,3,4,6,8,12,16,24,48
Factors of 72
List of positive integer factors of 72 that divides 72 without a remainder.
1,2,3,4,6,8,9,12,18,24,36,72
Factors of 84
List of positive integer factors of 84 that divides 84 without a remainder.
1,2,3,4,6,7,12,14,21,28,42,84
Factors of 300
List of positive integer factors of 300 that divides 300 without a remainder.
1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,150,300
Greatest Common Factor
We found the factors 48,72,84,300 . The biggest common factor number is the GCF number.
So the greatest common factor 48,72,84,300 is 12.
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 7/48, 1/72, 75/84, 14/300?
Answer: LCM of Numerators as per given numbers 7/48, 1/72, 75/84, 14/300 is
LCM of Numerators i.e. for 7,1,75,14 is 1050
GCF of denominators i.e. for 48,72,84,300 is 12.
Thus, LCM of Fractions is 1050/12.Finally, LCM of Fractions for 7/48, 1/72, 75/84, 14/300 is 1050/12.