Mary is buying cups, plates and forks for her party. Cups are sold 6 in a package, plates are sold 9 in a package and forks are sold 10 in a package. If she wants to have the same number of each item for her party, what is the smallest number of packages of each that she should buy?

To solve this, we consider the Lowest common multiple (LCM) of the three numbers and divide this LCM by each number to get the lowest number of packages of each that she should buy to obtain equal number of items. By using the LCM format, we have

Factors........10-----9-----6

2....................5-----9-----3

3....................5-----3-----1

3....................5-----1-----1

5....................1-----1-----1

To get LCM, we Multiply all the entries we have under the column that contains the factors, that is:

LCM = 2*3*3*5 = 90.

Since we have 6cups in a package, 9 plates in a package and 10 forks in a package, to make sure we have equal number of items, we must divide 90 by the number of items in a package so as to get the amount of packages to be bought.

That is:

number of cup package to be bought = 90/6 = 15packages

number of plate package to be bought = 90/9 = 10packages

number of fork package to be bought = 90/10 = 9packages

This makes us have equal number of the items.