Copenhagen Urban Trains - Travel strip of journeys
If you don't need museum entry etc. or if you're not buzzing around the city all day, then you don't need a Copenhagen Card, instead you can buy a strip of train journeys for 125 DKK, called a "2 Zoner". Buy it from the machines at the stations with your credit card or coins. E.g. if your trip is across 4 zones then clip it twice (2 * 2 zones).
This tip has the address "Any station in the urban area"