LCM of 27 and 32
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 27 and 32 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 864 as output. Here you can check the answer for Find the LCM of 27 and 32.
What is LCM of 27 and 32
Given Numbers are 27, 32
We can find the LCM of 27, 32 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 27 and 32
Multiples of 27 =27,54,81,108,135,162,189,216,243,270,297,324,351,378,405,432,459,
Multiples of 32 =32,64,96,128,160,192,224,256,288,320,352,384,416,448,480,512,544,
Now, get the least common multiple of 27, 32 which is 864
So, the LCM of 27, 32 is 864.
Least Common Multiple (LCM) of 27 and 32 with the help of Prime Factorisation
One method for determining the LCM of 27 and 32 is to compare the prime factorization of each number. You can find the prime factorization for each number by following the instructions below:
Here is 27's prime factorization:
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factors of 27 are 3.
27 = 33
And this is 32's prime factorization:
| 2 | 32 |
| 2 | 16 |
| 2 | 8 |
| 2 | 4 |
| 2 | 2 |
| 1 |
Prime factors of 32 are 2.
32 = 25
When comparing the prime factorization of these two numbers, look for the highest power to which each prime factor is raised. In this case, the following primary factors must be considered:3,2
.25×33 = 864
This shows that the LCM of 27 and 32 is 864.
How to Calculate the LCM of 27 and 32 Using Common Multiples
The first step in determining the Least Common Multiple of 27 and 32 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 27 and 32:
Lets look at the first ten multiples of these numbers, 27 and 32:
27,54,81,108,135,162,189,216,243,459 are the first ten multiples of 27.
32,64,96,128,160,192,224,256,288,544 are the first ten multiples of 32.
You can continue to list the multiples of these numbers until you find a match. Once you have found a match, or several matches, the Least Common Multiple is the smallest of these matches. The first matching multiple(s) of 27 and 32, for example, are 324, 459, and 512. 864 is the least common multiple since it is the smallest.
27 and 32 have an LCM of 864.
Least Common Multiple of 27 and 32 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27 and 32, than apply into the LCM equation.
GCF(27,32) = 1
LCM(27,32) = ( 27 × 32) / 1
LCM(27,32) = 864 / 1
LCM(27,32) = 864
Related Least Common Multiples of 27
Related Least Common Multiples of 32
Frequently Asked Questions on LCM of 27 and 32
1. What is the LCM of 27 and 32?
The LCM of 27 and 32 is 864.
2. How to find the lowest common multiple of 27 and 32?
To find the lowest common multiple of 27 and 32, we have to get the multip;es of both numbers and identify the least common multiple in them which is 864.
3. What are the Factors of 27?
Answer: Factors of 27 are 1, 3, 9, 27. There are 4 integers that are factors of 27. The greatest factor of 27 is 27.
4. What are the Factors of 32?
Answer: Factors of 32 are 1, 2, 4, 8, 16, 32. There are 6 integers that are factors of 32. The greatest factor of 32 is 32.
5. How to Find the LCM of 27 and 32?Answer:
Least Common Multiple of 27 and 32 = 864
Step 1: Find the prime factorization of 27
27 = 3 x 3 x 3
Step 2: Find the prime factorization of 32
32 = 2 x 2 x 2 x 2 x 2
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 864 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3
Step 4: Therefore, the least common multiple of 27 and 32 is 864.