Ha, I wish to change my answer.
I was thinking of how common denominators would affect the answer during lunch and I suddenly realised that Jupiter's 3 inner moons were said to be in a fixed orbital resonance.
See:
http://www.planetary.org/multimedia/...ean-moons.html
If this is strictly true (I find this confusing because when I do the maths, the times are slightly out); then the 3 inner moons repeat their same pattern every orbit of Ganymede. (also note from the website illustration that they never seem to line up in a straight line!)
Anyway, the resonance means that one would only multiply Ganymedes orbital time by Callisto's to obtain the answer: 7.155 *16.689 = 119.409 days.
Maybe... because it also depends on frames of reference. Sidereal cycle was mentioned, but I have ignored any affect of Jupiter's 12 year orbit around the Sun, as that would do my head in!