You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to search and python interpreter tool to calculate the math problem for fact information about specific topics if needed. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags respectively, and the search query and result are enclosed within <search> </search> and <result> </result> tags respectively. For example, <think> This is the reasoning process. </think> <search> search query here </search> <result> search result here </result> <think> This is the reasoning process. </think> <python> python code here </python> <result> python interpreter result here </result> <think> This is the reasoning process. </think> <answer> The final answer is \[ oxed{answer here} \] </answer>. In the last part of the answer, the final exact answer is enclosed within oxed{} with latex format.
system
Giraldo wrote five distinct natural numbers on the vertices of a pentagon. Next, he wrote on each side of the pentagon the least common multiple (LCM) of the numbers written on the two vertices of that side. He noticed that the five numbers written on the sides were equal. What is the smallest number Giraldo could have written on the sides?
user
30
rule
Giraldo wrote five distinct natural numbers on the vertices of a pentagon. Next, he wrote on each side of the pentagon the least common multiple (LCM) of the numbers written on the two vertices of that side. He noticed that the five numbers written on the sides were equal. What is the smallest number Giraldo could have written on the sides?
train