A party store sells large plates in packs of 12 and small plates in packs of 8. In order to have an equal number of both, what is the least amount of large plants that would have to be purchased

In order to have the least amount of each, you would need to purchase 2 packages of large plates. Here is the reasoning:

You can buy the following number of large plates and small plates:

Small: 8, 16, 24, 32, ...

Large: 12, 24, 36, ...

The smallest number that can be bought so you have an equal amount is 24 of each.

To get 24 large plates, you would need 2 packages.