How many three digit numbers are there such that the digits are non-zero, the tens digit is a multiple of the hundreds digit, the units digit is a multiple of the tens digit, and none of the digits are the same?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
How many three digit numbers are there such that the digits are non-zero, the tens digit is a multiple of the hundreds digit, the units digit is a multiple of the tens digit, and none of the digits are the same?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
7
How many three digit numbers are there such that the digits are non-zero, the tens digit is a multiple of the hundreds digit, the units digit is a multiple of the tens digit, and none of the digits are the same?
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