The Ancient Wizard Albus owns 3 ancient Clocks of Perpetual Motion. Every day, Clock #1 runs 20 minutes fast; Clock #2 runs 30 minutes fast, and Clock #3 runs 40 minutes fast. He sets all three clocks to the correct time and leaves to visit his friend. After many days, he returns home and, to his surprise, finds all 3 clocks showing the correct time again! What is the fewest possible number of days Albus could have spent away from home?
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