Running gmod on HL2:DM or Lost Coast?

Help ok well the thing is im trying to buy garrys mod off steam and now when i click continue after entering it all it says i havent got any games it can be used with.

i got: Half life 2: Deathmatch and Half life 2: Lost coast

Why cant i buy it, im currently reinstalling half life 2 deathmatch, Please hellpp!!

[editline]09:48PM[/editline]

im sorry this is in the wrong place, i will repost

You must have either Half-Life 2, Counter-Strike Source or Team Fortress 2. Sorry, Lost Coast does not count.

Person above me is wrong.
You can use any Source game on the list, excluding Left 4 Dead and Left 4 Dead 2, but you cannot use games that you received from a free offer.