83. Four cyclists. Four identical circles represent four gravel tracks. Four cyclists start from the center at noon. Each moves along their own circle at speeds: the first - 6 km/h, the second - 9, the third - 12, and the fourth - 15 km/h. They agreed to ride until they all meet again at the center for the fourth time. The length of each circular track is $\frac{1}{3}$ km.

![](https://cdn.mathpix.com/cropped/2024_05_21_56f37ca27ac3d928838dg-028.jpg?height=548&width=537&top_left_y=805&top_left_x=765)

When will the meeting occur?
83. Cyclists \(A, B, C, D\) can ride one kilometer in \(\frac{1}{6}, \frac{1}{9}, \frac{1}{12}\) and \(\frac{1}{16}\) hours, respectively. Therefore, they complete a full lap in \(\frac{1}{18}, \frac{1}{27}\), and \(\frac{1}{45}\) hours and, thus, meet for the first time after \(\frac{1}{9}\) hours (or, equivalently, after \(6 \frac{2}{3}\) minutes). Four times \(6 \frac{2}{3}\) minutes is \(26 \frac{2}{3}\) minutes. Therefore, the fourth meeting of all four cyclists will occur at 12:26:40.