LCM of 3, 6 and 12 is 12. The method to find the smallest common multiple of two or more numbers is denoted as LCM. Students are recommended to follow the article of LCM with Examples to obtain in-depth knowledge of finding the least common multiple of given numbers. This article is well structured by expert faculty to provide the best study source to enhance effective learning of concepts among students. Let us study the simple method of finding the least common multiple of 3, 6 and 12 with a complete explanation in this article.
What is LCM of 3, 6 and 12?
The least common multiple of 3, 6 and 12 is 12.
How to Find LCM of 3, 6 and 12?
LCM of 3, 6 and 12 can be determined using the below three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 3, 6 and 12 Using Prime Factorisation Method
By prime factorisation method, we can write 3, 6 and 12 as the product of prime numbers, such that;
3 = 3
6 = 2 × 3
12 = 2 × 2 × 3
LCM (3, 6, 12) = 2 × 2 × 3 = 12
LCM of 3, 6 and 12 Using Division Method
In division method, to determine the LCM, we divide the numbers 3, 6 and 12 by their prime factors until we get the result as one in the complete row. The product of these divisors shows the least common multiple of 3, 6 and 12. This can be shown as below.
| 2 | 3 | 6 | 12 |
| 2 | 3 | 3 | 6 |
| 3 | 3 | 3 | 3 |
| x | 1 | 1 | 1 |
No more further division can be done.
Hence, LCM (3, 6, 12) = 2 × 2 × 3 = 12
LCM of 3, 6 and 12 Using Listing the Multiples
Here we list out the multiples of 3, 6 and 12 to calculate their least common multiple. The below table represents the multiples of 3, 6 and 12.
| Multiples of 3 | Multiples of 6 | Multiples of 12 |
| 3 | 6 | 12 |
| 6 | 12 | 24 |
| 9 | 18 | 36 |
| 12 | 24 | 48 |
| 15 | 30 | 60 |
| 18 | 36 | 72 |
LCM (3, 6, 12) = 12
Related Articles
Prime Factorisation and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
Q. 1: What is the smallest number that is divisible by 3, 6, and 12?
Solution: 12 is the smallest number that is divisible by 3, 6, and 12.
Q. 2: Find the LCM of 3, 6 and 12 by prime factorisation.
Solution: The LCM of 3, 6 and 12 using prime factorisation is shown below
3 = 3
6 = 2 × 3
12 = 2 × 2 × 3
LCM (3, 6, 12) = 2 × 2 × 3 = 12
Therefore the LCM of 3, 6 and 12 by prime factorisation is 12.
Frequently Asked Questions on LCM of 3, 6 and 12
What is the LCM of 3, 6 and 12?
What are the methods used to find the LCM of 3, 6 and 12?
The methods used to find the LCM of 3, 6 and 12 are as follows:
Prime Factorisation
Division Method
Listing Multiples
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