Utilize the LCM of Fractions Calculator to find the Least Common Multiple of Fractions 10/12, 15/24, 18/32, 32/54 easily i.e. 720 along with step by step procedure.
LCM of 10/12, 15/24, 18/32, 32/54 is 720
LCM(10/12, 15/24, 18/32, 32/54) = 720
Ex: 8/5, 3/5, 2/5 (or) 2/3, 5/7 (or) 3/5, 5/9, 7/3
Given Input Data is 10/12,15/24,18/32,32/54
As per the formula LCM of Fractions = LCM of Numerators/GCF of Denominators
LCM of Numerators means (10,15,18,32) in this case as per given inputs
Least Common Multiple of 10,15,18,32 is 1440 the smallest number that is divisible by the numbers
GCF of Denominators means (12,24,32,54) in this case as per given inputs
Greatest Common Factor of 12,24,32,54 is 2 the largest number by which both the numbers can be divided
Lets's calculate LCM of 10,15,18,32
Arrange the Inputs 10,15,18,32 in a horizontal line separated by commas and divide them with a prime number. Note the quotients in the next row and divide with quotients with prime numbers again. Continue the process until you have all co primes in the last.
2 | 10, 15, 18, 32 |
3 | 5, 15, 9, 16 |
5 | 5, 5, 3, 16 |
1, 1, 3, 16 |
As all the numbers left in the last row are co primes you need not do the common division process further.
To obtain the Least Common Multiple, multiply the prime numbers with which you have divided the given numbers and the co primes in the last row i.e. 2 x 3 x 5 x 1 x 1 x 3 x 16 = 1440
Therefore, LCM of 10,15,18,32 is 1440
Step1:
Let's calculate the LCM of first two numbers
The formula of LCM is LCM(a,b) = ( a x b) / GCF(a,b)
GCF(10, 15) = 5
LCM(10, 15) = ( 10 x 15 ) / 5
LCM(10, 15) = 150 / 5
LCM(10, 15) = 30
Step2:
Here we consider the LCM from the above i.e. 30 as first number and the next as 18
The formula of LCM is LCM(a,b) = ( a x b) / GCF(a,b)
GCF(30, 18) = 6
LCM(30, 18) = ( 30 x 18 ) / 6
LCM(30, 18) = 540 / 6
LCM(30, 18) = 90
Step3:
Here we consider the LCM from the above i.e. 90 as first number and the next as 32
The formula of LCM is LCM(a,b) = ( a x b) / GCF(a,b)
GCF(90, 32) = 2
LCM(90, 32) = ( 90 x 32 ) / 2
LCM(90, 32) = 2880 / 2
LCM(90, 32) = 1440
LCM of 10,15,18,32 is 1440
Lets's calculate GCF of 12,24,32,54
2 | 12, 24, 32, 54 |
6, 12, 16, 27 |
∴ So the GCF of the given numbers is 2
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 1440/2
Therefore the LCM of Fractions 10/12,15/24,18/32,32/54 is 720
Factors of 12
List of positive integer factors of 12 that divides 12 without a remainder.
1,2,3,4,6,12
Factors of 24
List of positive integer factors of 24 that divides 24 without a remainder.
1,2,3,4,6,8,12,24
Factors of 32
List of positive integer factors of 32 that divides 32 without a remainder.
1,2,4,8,16,32
Factors of 54
List of positive integer factors of 54 that divides 54 without a remainder.
1,2,3,6,9,18,27,54
Greatest Common Factor
We found the factors 12,24,32,54 . The biggest common factor number is the GCF number.
So the greatest common factor 12,24,32,54 is 2.
Here are some samples of LCM of Fractions calculations.
1. What is the LCM of Fractions 10/12, 15/24, 18/32, 32/54?
LCM of Fractions 10/12, 15/24, 18/32, 32/54 is 720.
2. How to find LCM of Fractions 10/12, 15/24, 18/32, 32/54?
You can find the LCM of Fractions 10/12, 15/24, 18/32, 32/54 by dividing the LCM of Numerators (10,15,18,32) with GCF of Denominators(12,24,32,54).
3. Where do I get a detailed procedure for finding the LCM of Fractions 10/12, 15/24, 18/32, 32/54?
You can get a detailed procedure for finding the LCM of Fractions 10/12, 15/24, 18/32, 32/54 on our page.