Grace wants to make a bow and needs to cut two ropes with lengths of $$45$$ cm and $$30$$ cm into small pieces of equal length without leaving any surplus. What is the longest possible length of each piece?~\uline{~~~~~~~~~~}~$$\text{cm}$$     Candy thinks about this and says, "I think the longest possible length of each piece is $$180\text{cm}$$." Is she correct? If not, find the correct solution to the above problem. 
Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples