LCM of 3, 5 and 9 is 45. LCM stands for Least Common Multiple or the Lowest Common Multiple also known as LCD Least Common Divisor is the positive number that is a common multiple to the given set of numbers. Here the given set of numbers are 3, 5 and 9. 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 3, 5 and 9
The Least Common Multiple or Lowest Common Multiple of 3, 5 and 9 is 45.
How to Find LCM of 3, 5 and 9?
LCM of 3, 5 and 9 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 3, 5 and 9 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 3, 5 and 9 can be expressed as;
3 = 1 × 3
5 = 1 × 5
9 = 3 × 3
The product of 3, 5 and 3 forms the LCM
LCM(3, 5 and 9) = 3 × 3 × 5 = 45
LCM of 3, 5 and 9 Using Division Method
In the Division Method, the given numbers 3, 5 and 9 are divided by common prime divisors. Since 3, and 5 are prime numbers these are multiplied by the other prime factor of 9 to get the LCM.
|
3 |
3 |
5 |
9 |
|
3 |
1 |
5 |
3 |
|
5 |
1 |
5 |
1 |
|
× |
1 |
1 |
1 |
LCM(3, 5 and 9) = 3 × 3 × 5 = 45
LCM of 3, 5 and 9 Using Listing the Multiples
By listing all the multiples of 3, 5 and 9, we can observe the LCM. Below is the list of multiples for 3, 5 and 9.
|
Multiples of 3 |
Multiples of 5 |
Multiples of 9 |
|
3 |
5 |
9 |
|
6 |
10 |
18 |
|
9 |
15 |
27 |
|
12 |
20 |
36 |
|
15 |
25 |
45 |
|
18 |
30 |
54 |
|
21 |
35 |
63 |
|
24 |
40 |
72 |
|
27 |
45 |
81 |
|
30 |
50 |
90 |
|
33 |
55 |
99 |
|
36 |
60 |
108 |
|
39 |
65 |
117 |
|
42 |
70 |
126 |
|
45 |
75 |
135 |
LCM(3, 5 and 9) = 45
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 3, 5 and 9?
Answer: 45 is the smallest number that is divisible by 3, 5 and 9.
What is the LCM of 3 and 45?
Answer: LCM of 3 and 45 is 45.
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