If $x$, $y$, and $z$ are positive with $xy=24$, $xz = 48$, and $yz=72$, what is the value of $x+y+z$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
If $x$, $y$, and $z$ are positive with $xy=24$, $xz = 48$, and $yz=72$, what is the value of $x+y+z$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
22
If $x$, $y$, and $z$ are positive with $xy=24$, $xz = 48$, and $yz=72$, what is the value of $x+y+z$?
train