Final answer:
The integrated circuit (microchip) was the most crucial component that made possible the development of personal computers (PCs).
Step-by-step explanation:
The most crucial component that made possible the development of personal computers (PCs) was the integrated circuit (microchip). The invention of the microchip allowed for the miniaturization and integration of computer components onto a single chip, which significantly reduced the size and cost of computers. The integrated circuit revolutionized computing by holding all the processing power of a computer in a single circuit, making it possible to build affordable personal computers.