LCM of 9 and 21 is 63 . The least common multiple of 9 and 21 can be understood by examining their multiples (9, 18, 27, 36, 45, 54, ….) and (21, 42, 63, 84, 105,….) respectively. The LCM of two numbers can be determined using various methods such as prime factorisation, division, and listing the multiples.
Also read: Least common multiple
The LCM of 9 and 21 is 63. This article illustrates the processes involved in determining the LCM of 9 and 21. The LCM of these two non-zero integers is the smallest positive integer (63 in this case) that is divisible by both 9 and 21 without leaving a remainder.
The LCM of 9 and 21 can be calculated using the following methods:
The prime factorisation of 9 and 21, respectively, are as follows:
9 = 3 x 3 = 3²
21 = 3 x 7 = 3¹ x 7¹
LCM (9, 21) = 63
The LCM of 9 and 21 can be found using the division method, where we divide the numbers by their common prime factors. The LCM is then calculated by multiplying these divisors.
| 3 | 9 | 21 |
| 3 | 3 | 7 |
| 7 | 1 | 1 |
| x | 1 | 1 |
No further division is possible.
Hence, LCM (9, 21) = 63
The LCM of 9 and 21 can be found by listing out the multiples of both numbers and identifying the smallest common multiple.
| 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
What is the LCM of 9 and 21?
The LCM of 9 and 21 is 63. To get the LCM value, we should first find the multiples of 9 and 21 and the value which is divisible by 9 and 21 has to be determined.
What methods can be used to find the LCM value of 9 and 21?
The methods which can be used to find the LCM of 9 and 21 are Division Method, Prime Factorization Method and Listing multiples.
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. So, 63 x GCF = 189. Therefore, GCF = 189/63 = 3.