One of the cultures in my story lives on the dark side of a tidally locked planet. I had an idea that they would mark longer spans of time by the appearance of the three outer planets in the system in the sky. For example, every time the closest planet appears in the sky marks a "week", the next one a "month", etc.
An idea I had was that this culture would call a general assembly of chieftains (like the early Icelandic Althing) every time the three outer planets meet at the same point in the sky.
My planet orbits a red dwarf star and has an orbital period of approximately 48 hours. The system is loosely based on the Trappist 1 system, but you don't have to strictly stick to that in your answers. For context, the outer three planets of the Trappist 1 system have respective orbital periods of roughly 9, 12, and 19 days.
What would the ratios of the planets' orbits have to be for this meeting to happen roughly every 1-2 Earth years?