LCM of 12, 15 and 45 is 180. LCM stands for Least Common Multiple or the Lowest common multiple also known as LCD Least Common Divisor is the positive integer that is a common multiple to the given set of numbers. Here the given set of numbers are 12, 15 and 45. The smallest common multiple for all these numbers among many is 180, and hence it is the LCM. You can use the LCM with Examples to understand more on LCM.
What is LCM of 12, 15 and 45
The Least Common Multiple or Lowest Common Multiple of 12, 15 and 45 is 180.
How to Find LCM of 12, 15 and 45?
LCM of 12, 15 and 45 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 12, 15 and 45 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 12, 15 and 45 can be expressed as;
12 = 2 × 2 × 3
15 = 3 × 5
45 = 3 × 3 × 5
LCM(12, 15 and 45) = 2 × 2 × 3 × 3 × 5 = 180
LCM of 12, 15 and 45 Using Division Method
In the Division Method, the given set of numbers are written in the same row separated by a comma. These numbers are divided with the smallest number that divides all, until no further division is possible or only when prime numbers are left.
|
2 |
12 |
15 |
45 |
|
2 |
6 |
15 |
45 |
|
3 |
3 |
15 |
45 |
|
3 |
1 |
5 |
15 |
|
5 |
1 |
5 |
5 |
|
× |
1 |
1 |
1 |
LCM(12, 15 and 45) = 2 × 2 × 3 × 3 × 5 = 180
LCM of 12, 15 and 45 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 12, 15 and 45
Multiples of 12
12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204…
Multiples of 15:
15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210…
Multiples of 45:
45, 90, 135, 180, 225, 270…
LCM(12, 15 and 45) = 180
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 12, 15 and 45?
Answer: 180 is the smallest number that is divisible by 12, 15 and 45.
What is the LCM of 5, 12, 15 and 45?
Answer: LCM of 5, 12, 15 and 45 is 180 as 5 is the factor of 15 and 45.
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