Its the end of the school year and a tenth grade civics class is planning a barbecue to celebrate. the class has drinks and desserts but needs to plan the number of hamburgers it needs to buy. hamburger patties are sold in packages of six hamburgers. hamburger tolls come in packages of eight rolls. what is the smallest number of hamburgers that should be purchased to have no rolls left over from a package

Alright so think of it this way. You want the number of hamburger patties to equal the number of rolls with as little packages as possible.
              # of Packages         # per package        total #
Patties               1            x               6              =     6    
Rolls                  1            x               8              =     8

As you see above, the total number of patties and rolls is related to the product of the number of packages and the number per package.
Therefore to answer this problem, just find the least common multiple of 6 and 8:

Multiples of 6: 6, 12, 18, 24, 36...
Multiples of 8: 8, 16, 24, 32, 40

24 is the least common multiple. To get to 24, you multiply 6 by 4 and 8 by 3. Therefore, you need 4 packages of 6 hamburgers, and 3 packages of 8 rolls.

This is confirmed in the table below:
               # of Packages         # per package        total #
Patties               4            x               6              =     24   
Rolls                  3            x               8              =     24