Answer :

LCM: when simplifying fractions
GCF: when you need to find the zeros (x intercepts) of equations like [tex] x^{2} +10x+25[/tex]

Some possible answers are:

The LCM is useful when adding or subtracting fractions. It is also useful when finding the number of times two given numbers will overlap; for example, if you plant red flowers every 2 feet and yellow flowers every 3 feet, at what distances would you plant both color of flowers?

The GCF is useful when simplifying fractions.