Solve the following math problem efficiently and clearly:

- For simple problems (2 steps or fewer):
Provide a concise solution with minimal explanation.

- For complex problems (3 steps or more):
Use this step-by-step format:

## Step 1: [Concise description]
[Brief explanation and calculations]

## Step 2: [Concise description]
[Brief explanation and calculations]

...

Regardless of the approach, always conclude with:

Therefore, the final answer is: $oxed{answer}$. I hope it is correct.

Where [answer] is just the final number or expression that solves the problem.

Problem: For the opening home game of the baseball season, the Madd Batters minor league baseball team offered the following incentives to its fans:

Every 75th fan who entered the stadium got a coupon for a free hot dog.

Every 30th fan who entered the stadium got a coupon for a free cup of soda.

Every 50th fan who entered the stadium got a coupon for a free bag of popcorn.

The stadium holds 4000 fans and was completely full for this game. How many of the fans at the game were lucky enough to receive all three free items?
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