LCM of 9 and 21 is 63. Students can learn the concept of the least common multiple of 9 and 21 using common multiples from the study materials at BYJU’S. (9, 18, 27, 36, 45, 54, ….) and (21, 42, 63, 84, 105,….) are the multiples of 9 and 21. The LCM of two numbers can be found using the prime factorisation method, by listing the multiples and division methods.
Also read: Least common multiple
What is LCM of 9 and 21?
The answer to this question is 63. The LCM of 9 and 21 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 9 and 21, is the smallest positive integer 63 which is divisible by both 9 and 21 with no remainder.
How to Find LCM of 9 and 21?
LCM of 9 and 21 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 9 and 21 Using Prime Factorisation Method
The prime factorisation of 9 and 21, respectively, is given by:
9 = 3 x 3 = 3²
21 = 3 x 7 = 3¹ x 7¹
LCM (9, 21) = 63
LCM of 9 and 21 Using Division Method
We’ll divide the numbers (9, 21) by their prime factors to get the LCM of 9 and 21 using the division method (preferably common). The LCM of 9 and 21 is calculated by multiplying these divisors.
3 | 9 | 21 |
3 | 3 | 7 |
7 | 1 | 7 |
x | 1 | 1 |
No further division can be done.
Hence, LCM (9, 21) = 63
LCM of 9 and 21 Using Listing the Multiples
To calculate the LCM of 9 and 21 by listing out the common multiples, list the multiples as shown below.
Multiples of 9 | Multiples of 21 |
9 | 21 |
18 | 42 |
27 | 63 |
36 | 84 |
45 | 105 |
54 | 126 |
63 | 147 |
72 | 168 |
The smallest common multiple of 9 and 21 is 63.
Therefore LCM (9, 21) = 63
Related Articles
Video Lesson on Applications of LCM
![](https://cdn1.byjus.com/wp-content/uploads/2022/04/Application-of-LCM.jpg)
LCM of 9 and 21 Solved Example
What is the LCM if the product of two numbers is 189 and the GCD is 3?
Solution:
It is given that
Product of two numbers = 189
GCD = 3
We know that
LCM x GCD = Product of two numbers
LCM = Product/GCD
LCM = 189/3
LCM = 63
Hence, the LCM is 63.
Frequently Asked Questions on LCM of 9 and 21
What is the LCM of 9 and 21?
What methods can be used to find the LCM value of 9 and 21?
Determine the GCF if the LCM of 9 and 21 is 63.
LCM x GCF = 9 x 21
Given
LCM of 9 and 21 = 63
63 x GCF = 189
GCF = 189/63 = 3
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