solution: Call the integers $n-1$, $n$, and $n+1$. Their mean is $n$; their product is $(n-1)(n)(n+1)=120$ and their product divided by their mean is $(n-1)(n+1)=24$. Dividing the first equation by the second, we get $n=5$. The largest of the three is $n+1=\boxed{6}$.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  The product of three consecutive integers is 120. That product divided by the mean of the three integers is 24. What is the largest of the three consecutive integers?
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 6
extra_info.question: The product of three consecutive integers is 120. That product divided by the mean of the three integers is 24. What is the largest of the three consecutive integers?
extra_info.split: test