Answer to Question #275905 in Combinatorics | Number Theory for Vishnu Kumar

Question

Three planets P1, P2, P3 orbit a star in a distant galaxy. The perihelion of a

planet is the point in the orbit of a planet that is closest to the star. The orbital periods

of P1, P2, P3 are 3, 5 and 11 years respectively. The most recent perihelia of these

planets were in the years shown in the table below. What is the next year in which all

three planets achieve perihelion simultaneously?

Answer 1

this is least common multiple of P_1, P₂ and P₃:

$3\cdot5\cdot11=165$

planets achieve perihelion simultaneously every 165 years