From this exchange it appears that the lights will not draw close to maximum watts/amps even while full on. This has helped ease my mind with regards to the maximum amount of power I could possibly see.
He didn't get the full current draw because he was connecting them up with crappy wires and the strip wasn't getting enough volts.
45 meters of LEDs at 60 LEDs/meter is 2700 LEDs.
At 60mA per LED (they're RGB color) that's 162 amps if you set them all to white.
Luckily for you they're connected in groups of 3 so the current is a third of that, 54 amps.
You shouldn't run a power supply at 100% rating if you expect it to last so you need a 75A, 12V power supply.
Next you need to think carefully about how to wire it.
You can't just connect 12V to one end of a 45m strip and expect 54 amps to go down it. It simply won't work. You need to connect it in sections and make sure you're not getting much voltage drop anywhere along the strip. If you see voltage drop ("droop") you need to chop it up more and run more power cables. This is how you figure out how to wire it - measuring the voltage along the strip and make sure it stays at 12V. If you see (eg.) 11V anywhere then you need to chop it up more and run more power cables.
Once it's wired up with little power losses you need one of those "amplifier" boxes for each section of LEDs, all hooked up to a central controller.