Peter's party zone sells cups in packages of 666 and plates in packages of 888.
shaniya is hosting a birthday party for her little sister and wants to have the same number of each item.
what is the least number of packages of plates shaniya needs to buy?

Prime factorize the two numbers:

666 = 2 x 3 x 3 x 37
888 = 2 x 2 x 2 x 3 x 37

Notice I lined up all the numbers into columns. If they appear for both numbers they are paired. The lowest common multiple is the product of all the unique columns:

LCM = 2 x 2 x 2 x 3 x 3 x 37 = 2664

You can use this strategy for as many numbers as you want. Also, you could find the greatest common factor by multiplying only the paired columns.