"not the least of which" refers to trying to pinpoint the moon's age as a compelling reason for another moon landing. The statement suggests that there are many reasons for the landing and that pinpointing the moon's age is one of the more important ones. It is not the least important reason. In your everyday life, a good example might be: "There are many things in my life which make me happy, not the least of which are the good friends I have made on italki." This would mean that, of the many things in life that make you happy, italki friends are higher on the list than the least important things. Here is another example: "There several reasons for learning to speak English fluently, not the least of which is getting a good job." This means that learning English well to get a good job is more important than some of the other reasons for learning English.

Here "not the least of which" means "one of the many reasons”. Where I'm from we don't really use "not the least of which" in daily life.