Let $m$ and $n$ be positive integers such that $m = 24n + 51$. What is the largest possible value of the greatest common divisor of $2m$ and $3n$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $m$ and $n$ be positive integers such that $m = 24n + 51$. What is the largest possible value of the greatest common divisor of $2m$ and $3n$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
102
Let $m$ and $n$ be positive integers such that $m = 24n + 51$. What is the largest possible value of the greatest common divisor of $2m$ and $3n$?
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