When the Swiss didn't have so much experience yet with making clocks, a painful mistake was made with a church clock. The clock was officially put into use when it showed 6 o'clock. But soon it was noticed that the hour hand and minute hand had been interchanged and attached to the wrong axes.

The result was that the hour hand moved with a speed precisely 23 times higher than the minute hand. When the clock maker arrived, a remarkable thing happened: on the moment he inspected the clock, it showed exactly the right time again.

If the clock started at 6 o'clock in the correct position, then what was the first moment that it showed the correct time again?