LCM of 9 and 12 is 36. In mathematics, the LCM of any two numbers is the value that is evenly divisible by the two values. To find the LCM of Two Numbers that is 9 and 12, you can use one of three methods: division, listing multiples, or prime factorization. The smallest number among all frequent multiples of 9 and 12 is the LCM of 9 and 12. (9, 18, 27, 36, 45, etc.) and (12, 24, 36, 48, 60, etc.) are the first few multiples of 9 and 12.
Also read: Least common multiple
What is LCM of 9 and 12?
The answer to this question is 36. The LCM of 9 and 12 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 9 and 12, is the smallest positive integer 36 which is divisible by both 9 and 12 with no remainder.
How to Find LCM of 9 and 12?
LCM of 9 and 12 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 9 and 12 Using Prime Factorisation Method
The prime factorisation of 9 and 12, respectively, is given by:
9 = 3 x 3 = 3²
12 = 2 x 2 x 3 = 2² x 31
LCM (9, 12) = 36
LCM of 9 and 12 Using Division Method
We’ll divide the numbers (9, 12) by their prime factors to get the LCM of 9 and 12 using the division method (preferably common). The LCM of 9 and 12 is calculated by multiplying these divisors.
| 2 | 9 | 12 |
| 2 | 9 | 6 |
| 3 | 9 | 3 |
| 3 | 3 | 1 |
| 1 | 1 |
No further division can be done.
Hence, LCM (9, 12) = 36
LCM of 9 and 12 Using Listing the Multiples
To calculate the LCM of 9 and 12 by listing out the common multiples, list the multiples as shown below
| Multiples of 9 | Multiples of 12 |
| 9 | 12 |
| 18 | 24 |
| 27 | 36 |
| 36 | 48 |
| 45 | 60 |
The smallest common multiple of 9 and 12 is 36.
LCM (9, 12) = 36
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Video Lesson on Applications of LCM
LCM of 9 and 12 Solved Example
The product of two numbers is 12. If their GCD is 1, what is their LCM?
Solution:
Given: GCD = 1
product of numbers = 12
LCM × GCD = product of numbers
Which implies LCM = Product/GCD = 12/1
Therefore, the LCM is 12.
The probable combination for the given case is LCM(3, 4) = 12.
Frequently Asked Questions on LCM of 9 and 12
What is the LCM of 9 and 12?
List the methods used to find the LCM of 9 and 12.
If the LCM of 12 and 9 is 36, Find its GCF.
Since the LCM of 12 and 9 = 36
⇒ 36 × GCF(12, 9) = 108
Therefore, the GCF = 108/36 = 3.
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