Why do this problem?
offers opportunities for pupils to reinforce their understanding of factors and multiples, and, in a simple example, see an illustration of 'lowest common multiple'. It would fit in well when revising multiplication tables or working on multiples and factors.
You could start on this problem with a whole class activity counting in, for example, $2$s and $5$s. When do you say the same number in both? Try also two numbers which have a common factor, for example, $4$s and $6$s. When do you say the same number first in both?
After this you could introduce the problem either verbally, as a printed sheet or on an interactive whiteboard. Once the children have understood what they are to do, they could work on it in pairs. Some children might benefit from using a calculator for this activity both for multiplying by $7$, and for checking results. You may wish to stop the class part way through to share some of the
different ways they are working and recording. Some may be drawing pictures, others may be listing numbers. You could talk about the benefits of the different ways and it may be that some children adopt other representations following this sharing process.
A discussion of methods and comparison of answers in a plenary may well bring up different results. This would be a good opportunity to discuss the meaning of lowest common multiple.
How many years does it take for these two moons to coincide?
Do these two moons coincide sooner than that?
Tell the children that more moons have been discovered circling Vuvv. Get them to work out the length of time between the super-eclipses if there are also moons that cycle taking $8, 9, 10 \ldots$ years.
Suggest starting with just three or four moons and slowly adding the higher numbers.