LCM of 6, 8 and 12 is 24. LCM can be defined as the least common multiple between two or more numbers which is wholly divisible by them. The article Least Common Multiple (LCM) is designed by experts so that students grasp the LCM concept in a better way. The main purpose of creating this article is to boost confidence in solving any type of question in an efficient manner. In this article, let us learn how to derive the least common multiple of 6, 8 and 12 in detail.
What is LCM of 6, 8 and 12?
The answer to this question is 24.
How to Find LCM of 6, 8 and 12?
The LCM of 6, 8 and 12 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 6, 8 and 12 Using Prime Factorisation Method
In the prime factorisation method, we can express the numbers as the product of prime numbers. Therefore, the numbers 6, 8 and 12 can be expressed as;
6 = 2 × 3
8 = 2 × 2 × 2
12 = 2 × 2 × 3
LCM (6, 8, 12) = 2 × 2 × 2 × 3 = 24
LCM of 6, 8 and 12 Using Division Method
In the division method, we divide the numbers 6, 8 and 12 by their prime factors until we get the result as one in the complete row to calculate their LCM. The product of these divisors represents the least common multiple of 6, 8 and 12.
| 2 | 6 | 8 | 12 |
| 2 | 3 | 4 | 6 |
| 2 | 3 | 2 | 3 |
| 3 | 3 | 1 | 3 |
| x | 1 | 1 | 1 |
No more further division can be done.
Hence, LCM (6, 8, 12) = 2 × 2 × 2 × 3 = 24
LCM of 6, 8 and 12 Using Listing the Multiples
Here, we list out the multiples of 6, 8 and 12 to find the least common multiple of 6, 8 and 12 with ease. Check the multiples of 6, 8 and 12 from the table mentioned below.
| Multiples of 6 | Multiples of 8 | Multiples of 12 |
| 6 | 8 | 12 |
| 12 | 16 | 24 |
| 18 | 24 | 36 |
| 24 | 32 | 48 |
| 30 | 40 | 60 |
LCM (6, 8, 12) = 24
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Example
Question: What is the smallest number that is divisible by 6, 8, 12 exactly?
Solution: The smallest number that is divisible by 6, 8,12 exactly is their LCM. The least common multiple of 6, 8 and 12 is 24. Therefore the smallest number that is divisible by 6, 8, 12 exactly is 24.
Frequently Asked Questions on LCM of 6, 8 and 12
Q1
What is the LCM of 6, 8 and 12?
The LCM of 6, 8 and 12 is 24.
Q2
Is the LCM of 6, 8 and 12 the same as the HCF of 6, 8 and 12?
No. The LCM of 6, 8 and 12 is 24 and the HCF of 6, 8 and 12 is 2.
Q3
44 is the LCM of 6, 8 and 12. True or False.
False. The LCM of 6, 8 and 12 is 24.
Q4
Name the method used to calculate the LCM of 6, 8 and 12.
The following methods are used to calculate the LCM of 6, 8 and 12
Prime Factorisation
Division Method
Listing the Multiples
Q5
Find the LCM of 6, 8 and 12 using Prime Factorisation.
6 = 2 × 3
8 = 2 × 2 × 2
12 = 2 × 2 × 3
LCM (6, 8, 12) = 2 × 2 × 2 × 3 = 24
Therefore the LCM of 6, 8 and 12 using Prime Factorisation is 24
