LCM of 12, 15, 20 and 54 is 540. LCM also known as Least Common multiple or Lowest common multiple is the smallest or the least positive integer that is divisible by the given set of numbers. Consider the example for finding the LCM of 12, 15, 20 and 54. The answer is 540. 540 is the first/smallest/least number that is commonly divisible by 12, 15, 20 and 54. You can use the Prime Factorization and Division method to find the LCM.
What is LCM of 12, 15, 20 and 54
The Least Common Multiple or Lowest Common Multiple of 12, 15, 20 and 54 is 540.
How to Find LCM of 12, 15, 20 and 54?
LCM of 12, 15, 20 and 54 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 12, 15, 20 and 54 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 12, 15, 20 and 54 can be expressed as;
12 = 2 x 2 x 3
15 = 3 x 5
20 = 2 x 2 x 5
54 = 2 x 3 x 3 x 3
LCM (12, 15, 20, 54) = 2 x 2 x 3 x 3 x 3 x 5 = 540
LCM of 12, 15, 20 and 54 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 |
20 |
54 |
|
2 |
6 |
15 |
10 |
27 |
|
3 |
3 |
15 |
5 |
27 |
|
3 |
1 |
15 |
5 |
9 |
|
3 |
1 |
5 |
5 |
3 |
|
5 |
1 |
5 |
5 |
1 |
|
x |
1 |
1 |
1 |
1 |
LCM (12,15, 20, 54) = 2 x 2 x 3 x 3 x 3 x 5 = 540
LCM of 12, 15, 20 and 54 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, 20 and 54
Multiples of 12:
12, 24, 36,….. 144, 156, 168, …. 252, 264, 276, …. 360, 372, 384,….. 456, 468,…540, 552,…
Multiples of 15:
15, 30, 45,…. 150, 165, … 255, 270, …. 345, 360, … 450, 465, 525, 540, 555, …
Multiples of 20:
20, 40, 60, … 180, 200, 220,…. 340, 360, 380,… 480, 500, 520, 540, 560…
Multiples of 54:
54, 108, 162, … 378, 432, 486, 540, …
LCM (12, 15, 20, 54) = 540
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 12, 15, 20 and 54?
Answer: 540 is the smallest number that is divisible by 12, 15, 20 and 54.
What is the LCM of 5, 6, 12, 15, 20 and 54?
Answer: LCM of 5, 6, 12, 15, 20 and 54 is 540.
Comments