What is the smallest integer value of $b$ such that $423_{10}$ expressed in base $b$ also has $3$ digits?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
What is the smallest integer value of $b$ such that $423_{10}$ expressed in base $b$ also has $3$ digits?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
8
What is the smallest integer value of $b$ such that $423_{10}$ expressed in base $b$ also has $3$ digits?
train