Lavinia has 9 glasses and 6 mugs. she would like to set them out in identical groups with none left over in preparation for a party. What is the greatest number of groups Lavinia can set out

You must find the factors of each number ...

9 = 1, 3, 3, 9

6 = 1, 2, 3, 6

Next, determine the common multiple ...

9 = 1, 3, 3, 9

6 = 1, 2, 3, 6

Therefore, the most groups Lavinia can make without any glasses or mugs left to spare is 3.