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[Krelos]

Allrighty, I'm working on detailing the moon phases for my novel, right, and I managed to give myself a problem I don't know how to solve in my mentally fatigued state.. or possibly at all. And basically, this place is what comes to mind when I think of smart people on the internet.
So here we go!

We have 2 moons, we'll call them M1 and M2. M2 makes a full orbit in 6.5 months and M1 in 4.
What I need to know is how long it takes for M1 to catch up to and lap M2.
Dear God I hope this isn't as simple as it sounds...

Anyway, if someone feels like shedding some light on me here, I'd really appreciate it!

[ed boy]

4x6.5=26
in 26 months, M2 will do four orbits and M1 will do 6.5
In 52 months, M2 will do 8 orbits and M1 will do 13.

This means that in a 52-month period, M1 will do 5 more orbits than M2.
This means that in a 10.2 month period, M1 will do 1 more orbit than M2.

Your answer is 10.2 months. The use of months will not work properly unless all months are the same length.

[Krelos]

Thanks much ed. My months are all the same length so that does indeed work.

Turned out to be just as simple as I feared it was... that's what I get for staying up all night again.