Let M be a complete Riemannian locally symmetric space of non-positive curvature and of finite volume. We show that there are only finitely many compact maximal flats in M of volume bounded by a given number. As a corollary in the case $M=\mathrm{SL}_n(\mathbb{Z})\backslash\mathrm{SL}_n(\mathbb{R})/\mathrm{SO}_n$, we give a different proof of a theorem of Remak that for any $n\in \mathbb{N}$, there are only finitely many totally real number fields of degree n whose regulator is less than a given number.