Question

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

Answer 1

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:
$\frac{48}{72}$ ÷ $\frac{24}{24}$ = $\frac{2}{3}$
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