solution: Let $M$ be the least positive multiple of 30 that can be written with only the digits 0 and 2. First, $M$ is a multiple of 10, so its units digit must be 0. $M$ is also a multiple of 3, which means the sum of its digits must be a multiple of 3. Therefore, we must take at least  three 2's. Since $M$ is minimal, we take exactly three 2's and do not have any additional 0's: $M=\boxed{2220}$.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  What is the least positive integer multiple of 30 that can be written with only the digits 0 and 2?
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 2220
extra_info.question: What is the least positive integer multiple of 30 that can be written with only the digits 0 and 2?
extra_info.split: test