Why would you need to find the GCF and LCM of a set of numbers?

Answer 1

They GCF and LCM are useful in working with fractions:

In simplifying a fraction dividing the numerator (top) and denominator (bottom) by the same number reduces the fraction. By dividing through by the GCF of the numerator and denominator the fraction cannot be simplified any further (except converting improper (top heavy) fractions to mixed numbers). For large numbers, it may not be obvious what are the common factors of the numerator and denominator so using a general algorithm to find their GCF makes this easier.

When adding or subtracting fractions a common denominator is needed. One number which is guaranteed to work is to multiply all the denominators together. However, this can lead to extremely large numbers which can be difficult with which to work and lead to a fraction that will require simplifying. By using the LCM as the new denominator (hence its alternative name of LCD - Lowest Common Denominator) it ensures the numbers shouldn't get too big and should be easier with which to work.