What types of problems can be solved using the gcf what types of problems can be solved using the least common multiple

The Least Common Multiple is used to add fractions with unlike denominators:
Three things can happen:
1/3 + 1/7 - the LCM is the product of the denominators (in this case 21)
2/8 + 3/16 - the LCM is the greater denominator  (in this case 16)
2/9 + 5/6 - the LCM is lower than the product of the denominators (in this case it is 18)

The Greatest Common Factor is used to reduce fractions quickly:
 ÷  = 
By using the GCF -in this case 24, I reduced the fraction in a single step.
If I kept dividing by 2/2 (not the GCF), it would take much longer:
48/72 = 24/36 = 12/18 = 6/9 and then I would still have to divide 6/9 by 3/3 to get 2/3