What is the largest $n$ such that $a = 2^{306} \cdot 3^{340}$ is a perfect $n$th power?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
What is the largest $n$ such that $a = 2^{306} \cdot 3^{340}$ is a perfect $n$th power?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
34
What is the largest $n$ such that $a = 2^{306} \cdot 3^{340}$ is a perfect $n$th power?
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