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Last.fm advises all users to change their passwords as a precaution. While the site makes reference to the breaches involving the two other sites, it does not say whether it believes the hacks may be connected.
How many accounts are affected is not know: a Last.fm spokesperson only would say that it affects "a small fraction" of the site's 40 million users worldwide.
With all these hacks, now is a good time to rethink your password strategy in total. While it may not help you in the event a hacker gets your password information from a site you use (like what has happened here), it may offer some additional protection.