LCM of 6 and 12 is 12. Among all common multiples of 6 and 12, the LCM of 6 and 12 is the smallest value. (6, 12, 18, 24,…) and (12, 24, 36, 48,…) are the first few multiples of 6 and 12. Listing multiples, division technique, and prime factorization are three typical methods for calculating the LCM of 6 and 12. The LCM of Two Numbers is the value that is evenly divisible by both of them in Mathematics.
Also read: Least common multiple
What is LCM of 6 and 12?
The answer to this question is 12. The LCM of 6 and 12 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 6 and 12, is the smallest positive integer 12 which is divisible by both 6 and 12 with no remainder.
How to Find LCM of 6 and 12?
LCM of 6 and 12 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 6 and 12 Using Prime Factorisation Method
The prime factorisation of 6 and 12, respectively, is given by:
6 = (2 × 3) = 21 × 31
and
12 = (2 × 2 × 3) = 22 × 31
LCM (6, 12) = 12
LCM of 6 and 12 Using Division Method
We’ll divide the numbers (6, 12) by their prime factors to get the LCM of 6 and 12 using the division method (preferably common). The LCM of 6 and 12 is calculated by multiplying these divisors.
2 | 6 | 12 |
2 | 3 | 6 |
3 | 3 | 3 |
1 | 1 |
No further division can be done.
Hence, LCM (6, 12) = 12
LCM of 6 and 12 Using Listing the Multiples
To calculate the LCM of 6 and 12 by listing out the common multiples, list the multiples as shown below:
Multiples of 4 | Multiples of 5 |
6 | 12 |
12 | 24 |
18 | 36 |
24 | 48 |
30 | 60 |
The smallest common multiple of 6 and 12 is 12.
LCM (6, 12) = 12
Related Articles
Video Lesson on Applications of LCM
![](https://cdn1.byjus.com/wp-content/uploads/2022/04/Application-of-LCM.jpg)
LCM of 6 and 12 Solved Example
The GCD and LCM of two numbers are 6 and 12 respectively. If one number is 6, find the other number.
Solution:
Let the other number be a.
∵ GCD × LCM = 6 × a
⇒ a = (GCD × LCM)/6
⇒ a = (6 × 12)/6
⇒ a = 12
Therefore, the other number is 12.
Frequently Asked Questions on LCM of 6 and 12
What are the Methods to Find LCM of 6 and 12?
Listing Multiples
Division Method
Prime Factorization Method
Which of the following is the LCM of 6 and 12? 20, 12, 32, 3
If the LCM of 12 and 6 is 12, Find its GCF.
Since the LCM of 12 and 6 = 12
⇒ 12 × GCF(12, 6) = 72
Therefore, the GCF (greatest common factor) = 72/12 = 6.
Comments