The next market is on June 27.

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How do you read "June 27"?
1. June twenty-seven
2. June twenty-seventh

3. The next market is on the 27th day of June.
4. The next market is on the 27th of June.
5. The next market is on the 27 of June.
[Which one is grammatically correct of the three?]

We might say either 1 or 2, but 2 is more common.

All are correct. 3 is clumsy. 4 is most commonly said. 5 is less correct and would not be used.