Final answer:
The smallest positive integer that is divisible by 12, 15, and 18 is 180.
Step-by-step explanation:
In order to find the smallest positive integer that is divisible by 12, 15, and 18, we need to find the least common multiple (LCM) of these three numbers.
The LCM is the smallest positive integer that is divisible by all the given numbers.
To find the LCM, we can start by listing the multiples of the largest number, which is 18:
=> 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234, 252, 270, 288, 306, 324, 342, 360, ...
We can see that the first number in this list that is also divisible by 12 and 15 is 180.
Therefore, the smallest positive integer that is divisible by 12, 15, and 18 is 180.