LCM of 3 and 6 is 6. The LCM is the value which is divisible evenly by the given two numbers. Least common multiple of 3 and 6 can be obtained from the common multiples of two numbers. (3, 6, 9, 12, 15, 18, 21, ….) and (6, 12, 18, 24, 30, 36, ….) are the multiples of 3 and 6. The LCM of two numbers can be determined by listing the multiples, prime factorization and by division method.
Also read: Least common multiple
What is LCM of 3 and 6?
The answer to this question is 6. The LCM of 3 and 6 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 3 and 6, is the smallest positive integer 6 which is divisible by both 3 and 6 with no remainder.
How to Find LCM of 3 and 6?
LCM of 3 and 6 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 3 and 6 Using Prime Factorisation Method
The prime factorisation of 3 and 6, respectively, is given by:
3 = 3¹
6 = 2 x 3 = 2¹ x 3¹
LCM (3, 6) = 6
LCM of 3 and 6 Using Division Method
We’ll divide the numbers (3, 6) by their prime factors to get the LCM of 3 and 6 using the division method (preferably common). The LCM of 3 and 6 is calculated by multiplying these divisors.
| 2 | 3 | 6 |
| 3 | 3 | 3 |
| 1 | 1 |
No further division can be done.
Hence, LCM (3, 6) = 6
LCM of 3 and 6 Using Listing the Multiples
To calculate the LCM of 3 and 6 by listing out the common multiples, list the multiples as shown below
| Multiples of 3 | Multiples of 6 |
| 3 | 6 |
| 6 | 12 |
| 9 | 18 |
| 12 | 24 |
LCM (3, 6) = 6
Related Articles
Video Lesson on Applications of LCM
LCM of 3 and 6 Solved Example
Question: What is the smallest number exactly divisible by 3 and 6?
Solution:
We know that
LCM is the smallest number exactly divisible by 3 and 6.
Multiples of 3 = 3, 6, 9, 12, 15, ….
Multiples of 6 = 6, 12, 18, 24, 30, …..
Hence, the LCM of 3 and 6 is 6.
Frequently Asked Questions on LCM of 3 and 6
What are the methods used to find the LCM of 3 and 6?
Using prime factorisation, find the LCM of 3 and 6.
To find the LCM, we first should know the factors
3 = 3
6 = 2 x 3
LCM is the product of prime factors raised to the highest exponent among 3 and 6.
LCM of 3 and 6 = 2¹ x 3¹ = 6
Find GCF if the LCM of 3 and 6 is 6.
LCM x GCF = 3 x 6
As the LCM = 6
6 x GCF = 18
GCF = 18/6 = 3
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