Magnets with broken local inversion symmetries are interesting candidates for chiral magnetic textures such as skyrmions and spin spirals. The property of these magnets is that each subsequent layer can possess a different Dzyaloshniskii-Moriya interaction (DMI) originating from the local inversion symmetry breaking. Given that new candidates of such systems are emerging, with the Van der Waals crystals and magnetic multilayer systems, it is interesting to investigate how the chiral magnetic textures depend on the number of layers and the coupling between them. In this article, we model the magnetic layers with a classical Heisenberg spin model, where the sign of the DMI alternates for each consecutive layer. We use Monte Carlo simulations to examine chiral magnetic textures and show that the pitch of magnetic spirals is influenced by the interlayer coupling and the number of layers. We observe even-odd effects in the number of layers, where we observe a suppression of the spin spirals for even layer numbers. We give an explanation for our findings by proposing a net DMI in systems with strongly coupled layers. Our results can be used to determine the DMI in systems with a known number of layers, and for new technologies based on the tunability of the spiral wave length.