LCM of 5, 9 and 15 is 45. The abbreviation LCM stands for Least Common Multiple. It can also be read as the Lowest common multiple. The other terminology meaning the same is LCD, Least Common Divisor. All these terms mean the same, which is that a smallest positive integer is a common multiple to the given set of numbers. Here the given set of numbers are 5, 9 and 15. The smallest common multiple for all these numbers among many is 45, and hence it is the LCM. You can refer to LCM with Examples to understand better.
What is LCM of 5, 9 and 15
The Least Common Multiple or Lowest Common Multiple of 5, 9 and 15 is 45.
How to Find LCM of 5, 9 and 15?
LCM of 5, 9 and 15 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 5, 9 and 15 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers are equated by the product of prime factors. Here, 5, 9 and 15 can be expressed as;
5 = 1 × 5
9 = 3 × 3
15 = 3 × 5
LCM(5, 9 and 15) = 3 × 3 × 5 = 45
LCM of 5, 9 and 15 Using Division Method
In the Division Method, the given set of numbers are divided by the smallest prime factors. The division is considered complete once the remainder is 1.
|
3 |
5 |
9 |
15 |
|
3 |
5 |
3 |
5 |
|
5 |
5 |
1 |
5 |
|
× |
1 |
1 |
1 |
LCM(5, 9 and 15) = 3 × 3 × 5 = 45
LCM of 5, 9 and 15 Using Listing the Multiples
In listing the multiples method, the multiples of all the numbers are noted. The smallest common multiple is considered as the LCM.
|
Multiple of 5 |
Multiple of 9 |
Multiple of 15 |
|
5 |
9 |
15 |
|
10 |
18 |
30 |
|
15 |
27 |
45 |
|
20 |
36 |
60 |
|
25 |
45 |
75 |
|
30 |
54 |
90 |
|
35 |
63 |
105 |
|
40 |
72 |
120 |
|
45 |
81 |
135 |
|
50 |
90 |
150 |
LCM(5, 9 and 15) = 45
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 5, 9 and 15?
Answer: 45 is the smallest number that is divisible by 5, 9 and 15.
What is the LCM of 3 and 45?
Answer: LCM of 3 and 45 is 45.
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