LCM of 9 and 21
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 9 and 21 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 63 as output. Here you can check the answer for Find the LCM of 9 and 21.
What is LCM of 9 and 21
Given Numbers are 9, 21
We can find the LCM of 9, 21 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 9 and 21
Multiples of 9 =9,18,27,36,45,54,63,72,81,90,99,108,117,126,135,144,153,
Multiples of 21 =21,42,63,84,105,126,147,168,189,210,231,252,273,294,315,336,357,
Now, get the least common multiple of 9, 21 which is 63
So, the LCM of 9, 21 is 63.
Least Common Multiple (LCM) of 9 and 21 with the help of Prime Factorisation
One method for determining the LCM of 9 and 21 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 21's prime factorization:
| 3 | 21 |
| 7 | 7 |
| 1 |
Prime factors of 21 are 3,7.
21 = 31×71
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:3,7
.32×71 = 63
This shows that the LCM of 9 and 21 is 63.
How to Calculate the LCM of 9 and 21 Using Common Multiples
The first step in determining the Least Common Multiple of 9 and 21 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 9 and 21:
Lets look at the first ten multiples of these numbers, 9 and 21:
9,18,27,36,45,54,63,72,81,153 are the first ten multiples of 9.
21,42,63,84,105,126,147,168,189,357 are the first ten multiples of 21.
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 21, for example, are 108, 153, and 336. 63 is the least common multiple since it is the smallest.
9 and 21 have an LCM of 63.
Least Common Multiple of 9 and 21 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 21, than apply into the LCM equation.
GCF(9,21) = 3
LCM(9,21) = ( 9 × 21) / 3
LCM(9,21) = 189 / 3
LCM(9,21) = 63
Related Least Common Multiples of 9
Related Least Common Multiples of 21
Frequently Asked Questions on LCM of 9 and 21
1. What is the LCM of 9 and 21?
The LCM of 9 and 21 is 63.
2. How to find the lowest common multiple of 9 and 21?
To find the lowest common multiple of 9 and 21, we have to get the multip;es of both numbers and identify the least common multiple in them which is 63.
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 21?
Answer: Factors of 21 are 1, 3, 7, 21. There are 4 integers that are factors of 21. The greatest factor of 21 is 21.
5. How to Find the LCM of 9 and 21?Answer:
Least Common Multiple of 9 and 21 = 63
Step 1: Find the prime factorization of 9
9 = 3 x 3
Step 2: Find the prime factorization of 21
21 = 3 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 63 = 3 x 3 x 7
Step 4: Therefore, the least common multiple of 9 and 21 is 63.