Fixed point theory is regarded as the foundation in mathematical analysis and applications. Finding a common fixed point has been a fundamental problem of self-mappings in various fields. In this project we studied the relationship between the metric space and the multiplicative metric spaces. Also, we explore the concept of common fixed point in both metric and multiplicative metric spaces. The research investigated the properties and existence of common fixed point under various conditions. We observed that fixed point and common fixed-point results in metric and multiplicative metric spaces under some contractive conditions are similar to those obtained in ordinary metric space.