A Local Area Network (LAN) requires a router to communicate over the Internet.
The router serves as a gateway that connects the LAN to the external network (Internet) and directs data traffic between the LAN and the Internet.
The other options:
Multiplexer combines multiple signals into one.
Repeater amplifies signals to extend the range.
Switch connects devices within the LAN but does not facilitate Internet communication.
Therefore, a router is the necessary device for a LAN to communicate over the Internet.
[References:, "Computer Networking: A Top-Down Approach" by James Kurose and Keith Ross, which explains network devices and their functions., "CCNA Routing and Switching Study Guide" by Todd Lammle, which covers routers and their roles in networks., , , , ]
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