Last.fm is a music streaming service and social network that uses your listening history to recommend new music and connect you with like-minded listeners. It was founded in 2002 and is currently owned by CBS Interactive.
It's likely that the Last.fm logo was created by incorporating ligatures into the letters "a" and "s" of the National typeface, which is a commercial font created by Klim Type Foundry. For additional information about the font, you can visit here.