Next alignment of planets with 40, 60, 90 year orbits

Three planets circle a star in the same plane and the same direction, with orbital periods of $40$, $60$ and $90$ years. Right now all three lie on one straight line through the star. Counting a line-up with planets on either side of the star as aligned, after how many years will they next be aligned?

$180$ years. Alignment means all angles agree modulo $180^\circ$, i.e. each planet is back on the same line after half its period: $20$, $30$ or $45$ years. The first common time is $\operatorname{lcm}(20,30,45)=180$.