LCM of 3, 9 and 18 is 18. LCM and LCD are both the same in terms of definition. LCM stands for Least/Lowest Common Multiple and LCD stands for Least Common Divisor. It is the positive integer that is a common multiple to the given set of numbers. Here the given set of numbers are 3, 9 and 18. The smallest common multiple for all these numbers among many is 18, and hence it is the LCM. 330, 660 are also the common multiples. You can refer to Multiples.
What is LCM of 3, 9 and 18
The Least Common Multiple or Lowest Common Multiple of 3, 9 and 18 is 18.
How to Find LCM of 3, 9 and 18?
LCM of 3, 9 and 18 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 3, 9 and 18 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 3, 9 and 18 can be expressed as;
3 = 1 × 3
9 = 3 × 3
18 = 2 × 3 × 3
Product of all the prime factors forms the LCM.
Since 3 is a factor for 9 and 18; and 9 is the factor of 18, 18 will be the LCM.
LCM (3, 9 and 18) = 2 × 3 × 3 = 18
LCM of 3, 9 and 18 Using Division Method
In the Division Method, the given set of numbers are divided with prime divisors till the remainders are 1. Product of the prime numbers forms the LCM.
|
2 |
3 |
9 |
18 |
|
3 |
3 |
9 |
9 |
|
3 |
1 |
3 |
3 |
|
× |
1 |
1 |
1 |
LCM (3, 9 and 18) = 2 × 3 × 3 = 18
LCM of 3, 9 and 18 Using Listing the Multiples
By listing all the multiples of given numbers, we can identify the first/smallest/least common multiple, which is the LCM. Below is the list of multiples for 3, 9 and 18
|
Multiple of 3 |
Multiple of 9 |
Multiple of 18 |
|
3 |
9 |
18 |
|
6 |
18 |
36 |
|
9 |
27 |
54 |
|
12 |
36 |
72 |
|
15 |
45 |
90 |
|
18 |
54 |
108 |
|
21 |
63 |
126 |
LCM (3, 9 and 18) = 18
Related Articles
- LCM
- HCF and LCM
- LCM Formula
- LCM Calculator
- Prime Factorization and Division method
- LCM with Examples
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 3, 9 and 18?
Answer: 18 is the smallest number that is divisible by 3, 9 and 18.
What is the LCM of 3 and 18?
Answer: LCM of 3 and 18 is 18 as a factor of 18.
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