LCM of 2, 3 and 6 is 6. The number which is equally divisible by 2, 3 and 6 gives the LCM value. The common multiples of the two numbers will help you obtain the least common multiple of 2, 3 and 6. The multiples of 2 are (2, 4, 6, 8, 10, 12, ….), the multiples of 3 are (3, 6, 9, 12, 15, 18, ……) and the multiples of 6 are (6, 12, 18, 24, 30, 36, …..) respectively. For more accurate details on the LCM concept and the methods such as prime factorisation, division and listing of the multiples used, kindly visit BYJU’S.
Also read: Least common multiple
What is LCM of 2, 3 and 6?
The answer to this question is 6. The LCM of 2, 3 and 6 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 2, 3 and 6, is the smallest positive integer 6 which is divisible by both 2, 3 and 6 with no remainder.
How to Find LCM of 2, 3 and 6?
LCM of 2, 3 and 6 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 2, 3 and 6 Using Prime Factorisation Method
The prime factorisation of 2, 3 and 6, respectively, is given by:
2 = 2 = 2¹
3 = 3 = 3¹
6 = 2 x 3 = 2¹ x 3¹
LCM (2, 3, 6) = 6
LCM of 2, 3 and 6 Using Division Method
We’ll divide the numbers (2, 3, 6) by their prime factors to get the LCM of 2, 3 and 6 using the division method (preferably common). The LCM of 2, 3 and 6 is calculated by multiplying these divisors.
| 2 | 2 | 3 | 6 |
| 3 | 1 | 3 | 3 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (2, 3, 6) = 6
LCM of 2, 3 and 6 Using Listing the Multiples
To calculate the LCM of 2, 3 and 6 by listing out the common multiples, list the multiples as shown below
| Multiples of 2 | Multiples of 3 | Multiples of 6 |
| 2 | 3 | 6 |
| 4 | 6 | 12 |
| 6 | 9 | 18 |
| 8 | 12 | 24 |
| 10 | 15 | 30 |
LCM (2, 3, 6) = 6
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LCM of 2, 3 and 6 Solved Examples
Question: Which is the smallest number divisible by 2, 3 and 6 exactly?
Solution:
The smallest number divisible by 2, 3 and 6 exactly is LCM.
Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, ……
Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, …..
Multiples of 6 = 6, 12, 18, 24, 30, 36, ……
Therefore, the LCM of 2, 3 and 6 is 6.
Frequently Asked Questions on LCM of 2, 3 and 6
Using prime factorisation, what is the LCM of 2, 3 and 6?
Using prime factorisation,
2 = 2 = 2¹
3 = 3 = 3¹
6 = 2 x 3 = 2¹ x 3¹
LCM (2, 3, 6) = 6
What is the LCM of 2, 3 and 6?
The LCM of 2, 3 and 6 is 6. The multiples of 2, 3 and 6 has to be found first to get the LCM value
Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, ……
Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, …..
Multiples of 6 = 6, 12, 18, 24, 30, 36, ……
The smallest multiple exactly divisible by 2, 3 and 6 is 6.
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