LCM of 3, 5 and 6 is 30. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. The smallest number among all frequent multiples of 3, 5, and 6 is the LCM of 3, 5, and 6. (3, 6, 9, 12, 15…), (5, 10, 15, 20, 25…), and (6, 12, 18, 24, 30…), respectively, are the first few multiples of 3, 5, and 6. There are three typical ways for calculating the LCM of 3, 5, and 6: division, prime factorization, and listing multiples.
Also read: Least common multiple
What is LCM of 3, 5 and 6?
The answer to this question is 30. The LCM of 3, 5 and 6 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 3, 5 and 6, is the smallest positive integer 30 which is divisible by both 3, 5 and 6 with no remainder.
How to Find LCM of 3, 5 and 6?
LCM of 3, 5 and 6 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 3, 5 and 6 Using Prime Factorisation Method
The prime factorisation of 3, 5 and 6, respectively, is given by:
(3) = 31,
(5) = 51, and
6 = (2 × 3) = 21 × 31
LCM (3, 5, 6) = 30
LCM of 3, 5 and 6 Using Division Method
We’ll divide the numbers (3, 5, 6) by their prime factors to get the LCM of 3, 5 and 6 using the division method (preferably common). The LCM of 3, 5 and 6 is calculated by multiplying these divisors.
| 2 | 3 | 5 | 6 |
| 3 | 3 | 5 | 3 |
| 5 | 1 | 5 | 1 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (3, 5, 6) = 30
LCM of 3, 5 and 6 Using Listing the Multiples
To calculate the LCM of 3, 5 and 6 by listing out the common multiples, list the multiples as shown below.
| Multiples of 3 | Multiples of 5 | Multiples of 6 |
| 3 | 5 | 6 |
| 6 | 10 | 12 |
| 9 | 15 | 18 |
| 12 | 20 | 24 |
| 15 | 25 | 30 |
| 18 | 30 | 36 |
| 21 | 35 | 42 |
| 24 | 40 | 48 |
| 27 | 45 | 54 |
| 30 | 50 | 60 |
The smallest common multiple of 3, 5 and 6 is 30.
Therefore LCM (3, 5, 6) = 30
Related Articles
Video Lesson on Applications of LCM
LCM of 3, 5 and 6 Solved Example
Question: Calculate the LCM of 3, 5, and 6 using the GCD of the given numbers.
Solution:
Prime factorization of 3, 5, 6:
3 = 3
5 = 5
6 = 2 × 3
Therefore, GCD(3, 5) = 1, GCD(5, 6) = 1, GCD(3, 6) = 3, GCD(3, 5, 6) = 1
We know,
LCM(3, 5, 6) = [(3 × 5 × 6) × GCD(3, 5, 6)]/[GCD(3, 5) × GCD(5, 6) × GCD(3, 6)]
LCM(3, 5, 6) = (90 × 1)/(1 × 1 × 3) = 30
⇒LCM(3, 5, 6) = 30
Comments