you have to purchase a license to be able to broadcast the music. There are various agencies that handle the licensing, each for a variety of artists.
here is a simple Google search you can start with:
https://www.google.com/search?q=licenses+for+broadcast+of+music&aq=f&oq=licenses+for+broadcast+of+music&aqs=chrome.0.57j0.9702j0&sourceid=chrome&ie=UTF-8#hl=en&sclient=psy-ab&q=licensing+music+for+broadcast&oq=licensing+music+for+broadcast&gs_l=serp.12..0i22i30.8446.12461.1.13726.13.5.0.1.1.4.156.560.1j4.5.0...0.0...1c.1.11.psy-ab.t7ODaC7rVxY&pbx=1&bav=on.2,or.r_qf.&bvm=bv.45645796,d.aWM&fp=1a317f44bff72960&biw=1237&bih=897
You can probably ask the DJ who he purchased his licenses from. If he didn't, then he shouldn't be doing what he is doing.