LCM of 15 and 16 is 240.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 16, 240 is the first(least or smallest) number that is common in the set of multiples of 15 and 16. The LCM is also known as LCD, Least Common Divisor. You can use the Prime Factorization and Division method to find the LCM of the given numbers.
What is LCM of 15 and 16
The Least Common Multiple or Lowest Common Multiple of 15 and 16 is 240.
How to Find LCM of 15 and 16?
LCM of 15 and 16 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 15 and 16 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 15 and 16 can be expressed as;
15 = 3 x 5
16 = 2 x 2 x 2 x 2
LCM (15, 16) = 2 x 2 x 2 x 2 x 3 x 5 = 240
LCM of 15 and 16 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 |
15 |
16 |
|
2 |
15 |
8 |
|
2 |
15 |
4 |
|
2 |
15 |
2 |
|
3 |
15 |
1 |
|
5 |
5 |
1 |
|
x |
1 |
1 |
The Division is complete. Hence, LCM (15, 16) = 2 x 2 x 2 x 2 x 3 x 5 = 240
LCM of 15 and 16 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 16
Multiples of 15: 15, 30, 45, …. 120, 135, ….210, 225, 240, 255 270..
Multiples of 16: 16, 32 48… 144 160… 224, 240, 256, 272…
LCM (15, 16) = 240
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 15 and 16?
Answer: 240 is the smallest number that is divisible by both 15 and 16.
What is the LCM for 5, 15 and 16?
Answer: LCM for 5, 15 and 16 is 240.
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