LCM of 15 and 20 is 60.The Least Common multiple or Lowest common multiple simply known as LCM is the smallest or the least positive integer that is divisible by the given set of numbers. In the given set of numbers 15 and 20, 60 is the first(least or smallest) number that is common in the set of multiples of 15 and 20. The LCM is also known as LCD, Least Common Divisor. You can refer to the LCM for more details.
What is LCM of 15 and 20
The Least Common Multiple or Lowest Common Multiple of 15 and 20 is 60.
How to Find LCM of 15 and 20?
LCM of 15 and 20 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 15 and 20 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 15 and 20 can be expressed as;
15 = 3 x 5
20 = 2 x 2 x 5
LCM (15, 20) = 2 x 2 x 3 x 5 = 60
LCM of 15 and 20 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.
|
5 |
15 |
20 |
|
2 |
3 |
4 |
|
2 |
3 |
2 |
|
3 |
3 |
1 |
|
x |
1 |
1 |
Hence, LCM (15, 20) = 2 x 2 x 3 x 5 = 60
LCM of 15 and 20 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 15 and 20
|
Multiples of 15 |
Multiples of 20 |
|
15 |
20 |
|
30 |
40 |
|
45 |
60 |
|
60 |
80 |
LCM (15, 20) = 60
Related Articles
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 15 and 20?
Answer: 60 is the smallest number that is divisible by both 15 and 20.
2. What is the LCM for 5, 15 and 20?
Answer: LCM for 5, 15 and 20 is 60.
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