Delta and KLM have a low $658 fare for flights from Los Angeles to Copenhagen via Amsterdam early next month. The LAX-CPH fare ranges from about $640 to $670 depending on month for travel from August into March 2016. The real deal here are flights in early August at $658 for summer 2015 travel.
Los Angeles LAX – Detroit DTW – Amsterdam AMS – Copenhagen, Denmark CPH/CPH – AMS – LAX
$657.80 Tuesday August 11 – Friday August 21
A two stop itinerary LAX-CPH is not best, but late summer flights tend to route more on Delta through USA hubs for the outbound. All KLM itineraries with LAX-AMS-CPH routing are possible on some dates.
Copenhagen does not have to be your final destination in Europe for a great deal. Low cost flights from CPH to other places in Europe are available for under $100 round trip. I am currently in London after a few days in Copenhagen and RyanAir round trip airfare was $63 USD all-in to London from Copenhagen.