LRMC=LRATC because the fixed cost component of ATC goes to zero as production approaches infinity.

I don't believe you can discover the LRMC just by looking at the production function Q=10KL. That production function will give you something like a production possibilities frontier if you try entering lots of different variables into it - so it tells you how much you CAN produce, but it doesn't say what it will cost.

I'm guessing there is some other information that you haven't posted. I'll save further comments until then.