In this paper we determine the delivery time for a multi-server coded caching problem when the cache size of each user is small. We propose an achievable scheme based on coded cache content placement, and employ zero-forcing techniques at the content delivery phase. Surprisingly, in contrast to previous multi-server results which were proved to be order-optimal within a multiplicative factor of 2, for the low memory regime we prove that our achievable scheme is optimal. Moreover, we compare the performance of our scheme with the uncoded solution, and show our proposal improvement over the uncoded scheme. Our results also apply to Degrees-of-Freedom (DoF) analysis of Multiple-Input Single-Output Broadcast Channels (MISO-BC) with cache-enabled users, where the multiple-antenna transmitter replaces the role of multiple servers. This shows that interference management in the low memory regime needs different caching techniques compared with medium-high memory regimes discussed in previous works.