What is the smallest positive five-digit integer, with all different digits, that is divisible by each of its non-zero digits?  Note that one of the digits of the original integer may be a zero.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
What is the smallest positive five-digit integer, with all different digits, that is divisible by each of its non-zero digits?  Note that one of the digits of the original integer may be a zero.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
10,\!236
What is the smallest positive five-digit integer, with all different digits, that is divisible by each of its non-zero digits?  Note that one of the digits of the original integer may be a zero.
train