Find the longest common prefix given two integer arrays.

Focus on breaking down the problem into manageable steps. Start by clarifying what is meant by "longest common prefix" in the context of integer arrays. Discuss potential edge cases, such as empty arrays or arrays of different lengths. Outline your approach to solving the problem, considering both time and space complexity. Be prepared to write pseudocode or actual code to demonstrate your solution, and explain your thought process as you go along, including any assumptions you make.