The greatest common divisor of positive integers $m$ and $n$ is 8. The least common multiple of $m$ and $n$ is 112. What is the least possible value of $m+n$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The greatest common divisor of positive integers $m$ and $n$ is 8. The least common multiple of $m$ and $n$ is 112. What is the least possible value of $m+n$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
72
The greatest common divisor of positive integers $m$ and $n$ is 8. The least common multiple of $m$ and $n$ is 112. What is the least possible value of $m+n$?
train