The main denominator is the smallest common multiple of two different fractions.
In order to reduce two fractions to one main denominator, you must first write down all the multiples of the denominators. Then you look at which numbers are multiples of both denominators and, if you find several, write down the smallest of these numbers. In order to expand the two fractions to the main denominator, you have to find out for both fractions which expansion number can be used to expand the denominators to the smallest common multiple.