  In this article, we prove that every arithmetic locally symmetric orbifold of
classical type without Euclidean or compact factors has arbitrarily long
arithmetic progressions in its primitive length spectrum. Moreover, we show the
stronger property that every primitive length occurs in arbitrarily long
arithmetic progressions in its primitive length spectrum. This confirms one
direction of a conjecture of Lafont--McReynolds, which states that the property
of having every primitive length occur in arbitrarily long arithmetic
progressions characterizes the arithmeticity of such spaces.
