Write a JavaScript program that takes in two integers as input and determines their greatest common divisor (GCD). The program should utilize the Euclidean algorithm to efficiently compute the GCD. The output should be displayed in the console or on the webpage, depending on implementation. The program should also handle edge cases, such as negative integers and zero values. Additionally, the code should be well-organized and properly commented for clarity and readability.
This prompt doesn't seem malicious.