LCM of 9 and 12
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 9 and 12 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 36 as output. Here you can check the answer for Find the LCM of 9 and 12.
What is LCM of 9 and 12
Given Numbers are 9, 12
We can find the LCM of 9, 12 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 9 and 12
Multiples of 9 =9,18,27,36,45,54,63,72,81,90,99,108,117,126,135,144,153,
Multiples of 12 =12,24,36,48,60,72,84,96,108,120,132,144,156,168,180,192,204,
Now, get the least common multiple of 9, 12 which is 36
So, the LCM of 9, 12 is 36.
Least Common Multiple (LCM) of 9 and 12 with the help of Prime Factorisation
One method for determining the LCM of 9 and 12 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 9's prime factorization:
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factors of 9 are 3.
9 = 32
And this is 12's prime factorization:
| 2 | 12 |
| 2 | 6 |
| 3 | 3 |
| 1 |
Prime factors of 12 are 2,3.
12 = 22×31
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
.22×32 = 36
This shows that the LCM of 9 and 12 is 36.
How to Calculate the LCM of 9 and 12 Using Common Multiples
The first step in determining the Least Common Multiple of 9 and 12 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 9 and 12:
Lets look at the first ten multiples of these numbers, 9 and 12:
9,18,27,36,45,54,63,72,81,153 are the first ten multiples of 9.
12,24,36,48,60,72,84,96,108,204 are the first ten multiples of 12.
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 9 and 12, for example, are 108, 153, and 192. 36 is the least common multiple since it is the smallest.
9 and 12 have an LCM of 36.
Least Common Multiple of 9 and 12 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9 and 12, than apply into the LCM equation.
GCF(9,12) = 3
LCM(9,12) = ( 9 × 12) / 3
LCM(9,12) = 108 / 3
LCM(9,12) = 36
Related Least Common Multiples of 9
Related Least Common Multiples of 12
Frequently Asked Questions on LCM of 9 and 12
1. What is the LCM of 9 and 12?
The LCM of 9 and 12 is 36.
2. How to find the lowest common multiple of 9 and 12?
To find the lowest common multiple of 9 and 12, we have to get the multip;es of both numbers and identify the least common multiple in them which is 36.
3. What are the Factors of 9?
Answer: Factors of 9 are 1, 3, 9. There are 3 integers that are factors of 9. The greatest factor of 9 is 9.
4. What are the Factors of 12?
Answer: Factors of 12 are 1, 2, 3, 4, 6, 12. There are 6 integers that are factors of 12. The greatest factor of 12 is 12.
5. How to Find the LCM of 9 and 12?Answer:
Least Common Multiple of 9 and 12 = 36
Step 1: Find the prime factorization of 9
9 = 3 x 3
Step 2: Find the prime factorization of 12
12 = 2 x 2 x 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 36 = 2 x 2 x 3 x 3
Step 4: Therefore, the least common multiple of 9 and 12 is 36.