Coinciding Comets

Comets 2P/Encke, 4P/Faye, and 8P/Tuttle have orbital periods of 3 years, 8 years, and 13 years, respectively. The last perihelions of each of these comets were in 2017, 2014, and 2008, respectively.

What is the next year in which all three of these comets will achieve perihelion in the same year?

For this problem, assume that time is measured in whole numbers of years and that each orbital period is constant.

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