The most common type of network topology in local area networks (LANs) is the star topology. In this configuration, all devices are connected to a central hub or switch, allowing for efficient communication and easy management. Star topology simplifies network troubleshooting and enhances performance, since a failure in one connection does not affect the entire network. Additionally, it facilitates easy addition of new devices without disrupting existing connections, making it a popular choice for both home and business networks.