Avril plans to make an artifact by using ribbons. She finds two ribbons with different length: $15$ $\text{cm}$ and $45$ $\text{cm}$. If she wants to cut both ribbons into short pieces of equal length such that there will be no surplus, what is the largest possible length of each short piece? 
Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples