Let a, b, c be three nonzero integers satisfying 7a + 11b + 13c = 0. What is the least possible value of |a| + |b| + |c|?
I tried graphing this on the x-y-z plane but that didn't help much as a, b, and c are integers. Could anyone explain how to solve this? I would also like to know the general strategy for solving this type of problem for the future.