Choosing k value in KNN classifier? I'm working on classification problem and decided to use KNN classifier for the problem.

so if k=131 gave me auc of 0.689 and k=71 gave me auc of 0.682 what should be my ideal k?

Does choosing higher k means more usage of computational resource? if that's the case can I go with k=71. (or) should I always use K with maximum score no matter what?
I was taught the best way is to find the error for each k then plot them and look for the "elbow" on the plot.