Meaning:

This is a humorous expression that is used when you found out someone else was thinking about the same thing as you were.

If you say, "Great minds think alike," you say, jokingly, that you and someone else must be very intelligent or great because both of you thought of the same thing or agree on something.

Example:

A: I'm going to the concert tonight.
B: Oh, really? Me too. I heard the performers are excellent.
A: Great minds think alike.

(A and B meet in a restaurant unexpectedly.)
A: How did you know I am here?
B: This restaurant is a very nice place to spend an evening. Great minds think alike.

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