Two comets, Alpha and Beta have periodic orbits with periods of exactly 76 years and 48 years respectively. When both comets appear in the same year, they are said to be in conjunction. How many years are between successive conjunctions?
Answer: Alpha returns in multiples of 76 years and Beta in multiples of 48 years. If we consider the year of a conjunction as year 0, then the subsequent conjunctions will occur in those years which are multiples of both 48 and 76, i.e. multiples of their least common multiple, lcm(48,76) = 912. Conjunction will occur every 912 years.
