Brightongirl
It is a couple of years since I have been to LAX but will do my best to answer.
Most departures to Europe turn to the south after take-off. I believe that this is to avoid conflicting with inbound traffic from the north. If departing from the southern runways (25R) then they will initially fly a heading of 250 and then turn onto a heading of 220 when passing the SMO (santa Monica) 160 radial. If departing from the northern runways (24L) they will head 250 until the controller tells them to turn left, generally onto a heading of about 220.
When the controller is satisfied that they have sufficient height, he will turn them left towards Seal Beach VOR. After Seal Beach they will turn left towards another VOR such as Daggett and then they proceed on course.
The distance that they fly out over the Pacific depends on how well they are climbing as they must be at about 14,000ft on reaching Seal Beach so that they pass over the inbound traffic to 24R and 25L.
Hope this helps.
Airclues