My question is simply how long it takes for the 7 known planets in Trappist-1 to be in the same configuration in relation to their host star, and to each-other. Those seven planets are in a 2:3:4:6:9:15:24 resonance, which is just extraordinary. I thought that they would be configured in the same manner roughly every 36 days, but I am not sure I did it right. I basically thought, "if all their orbital ratios are perfect, then I only need to see how long it takes for one of the planets to go through the amount of orbits listed in said ratio, and then I'll get my answer." I know that the answer I am looking for won't be exactly perfect, I am just wanting to know when they will be in practically the same place.
The specific calculation I did was take the orbital period of the sixth planet, say that 1/12th of that orbit was a "day"(instead of using earth days) and then multiplied it by the number of orbits that it has in the ratio (3) and got my answer. (36) I know this doesn't answer it in earth days, but since I am using that "orbit of #6/12 as the daylength in the story I am writing in this world, I am using the measuring stick that matters to my situation. So, am I right? Does it take 36 "days" for Trappist-1 to reconfigure itself, or did I get the math terribly wrong?