LCM of 3, 6 and 9 is 18. The least common multiple of two numbers is the smallest number which is a multiple of both the numbers. The article LCM of Two Numbers is the best resource as it helps students to understand the LCM concept easily. Following this article while solving problems is the ultimate need for students who intend to score good marks in exams. Let us understand the method of finding the least common multiple of 3, 6 and 9 with FAQs and solved examples in this article.
What is LCM of 3, 6 and 9?
The answer to this question is 18.
How to Find LCM of 3, 6 and 9?
The LCM of 3, 6, and 9 can be determined by using the methods mentioned below:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 3, 6 and 9 Using Prime Factorisation Method
The prime factorisation method is one of the most common ways of determining LCM. To calculate the LCM of 3, 6 and 9, we use the steps as follows:
3 = 3
6 = 2 × 3
9 = 3 × 3
LCM (3, 6, 9) = 2 × 3 × 3 = 18
LCM of 3, 6 and 9 Using Division Method
In this method, we divide the numbers 3, 6 and 9 by their prime factors until we get the result as one in the complete row to find their LCM. The product of these divisors gives the least common multiple of 3, 6 and 9.
| 2 | 3 | 6 | 9 |
| 3 | 3 | 3 | 9 |
| 3 | 1 | 1 | 3 |
| x | 1 | 1 | 1 |
No more further division can be done.
Hence, LCM (3, 6, 9) = 2 × 3 × 3 = 18
LCM of 3, 6 and 9 Using Listing the Multiples
In this method, the multiples of each number are listed until the first common multiple is found. The following table shows the multiples of 3, 6 and 9.
| Multiples of 3 | Multiples of 6 | Multiples of 9 |
| 3 | 6 | 9 |
| 6 | 12 | 18 |
| 9 | 18 | 27 |
| 12 | 24 | 36 |
| 15 | 30 | 45 |
| 18 | 36 | 54 |
| 21 | 42 | 63 |
LCM (3, 6, 9) = 18
Related Articles
Prime Factorization 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 9 exactly?
Solution: 18 is the smallest number that is divisible by 3, 6 and 9.
Q. 2: Find the LCM of 3, 6 and 9 using listing the multiples.
Solution: We can determine the least common multiple of 3, 6 and 9 using listing multiples as below.
First list the multiples of 3, 6, and 9
Multiples of 3 = 3, 6, 9, 12, 15, 18, 21,…..
Multiples of 6 = 6, 12, 18, 24, 30, 36,…..
Multiples of 9 = 9, 18, 27, 36, 45, 54, ……
Here, the lowest common multiple is 18
Hence, the least common multiple of 3, 6 and 9 is 18.
Frequently Asked Questions on LCM of 3, 6 and 9
What is the LCM of 3, 6 and 9?
Is the LCM of 3, 6 and 9 the same as the HCF of 3, 6 and 9?
Is 18 the LCM of 3, 6 and 9?
Calculate the LCM of 3, 6 and 9 using Prime Factorisation.
Here, we list the factors of 3, 6 and 9 to find the LCM
3 = 3
6 = 2 × 3
9 = 3 × 3
LCM (3, 6, 9) = 2 × 3 × 3 = 18
Write the methods used to determine the LCM of 3, 6 and 9.
The methods used to determine the LCM of 3, 6 and 9 are
Prime Factorisation
Division Method
Listing the Multiples
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