A loop invariant is a property of a loop that remains true before and after each execution of the loop. The identification of loop invariants is a critical step to support automated program safety assessment. Recent advancements in Large Language Models (LLMs) have demonstrated potential in diverse software engineering (SE) and formal verification tasks. However, we are not aware of the performance of LLMs to infer loop invariants. We report an empirical study of both open-source and closed-source LLMs of varying sizes to assess their proficiency in inferring inductive loop invariants for programs and in fixing incorrect invariants. Our findings reveal that while LLMs exhibit some utility in inferring and repairing loop invariants, their performance is substantially enhanced when supplemented with auxiliary information such as domain knowledge and illustrative examples. LLMs achieve a maximum success rate of 78\% in generating, but are limited to 16\% in repairing the invariant.