Jenny does the dishes every third day mark every fourth day and misty every sixth day if they all shared dish duty today when will they all share dish duty again?

Look at the multiples of these numbers.

3, 6, 9, 12, 15, 18, 21, 24

4, 8, 12, 15, etc.

6, 12, 18, etc.

What is the smallest multiple that the three share?

12

To determine when Jenny, Mark, and Misty will all share dish duty again, we need to find the least common multiple (LCM) of 3, 4, and 6. The LCM is the smallest number that is divisible by all three given numbers.

1. Let's list the multiples of each number until we find a common multiple:
- Multiples of 3: 3, 6, 9, 12, 15, 18, ...
- Multiples of 4: 4, 8, 12, 16, 20, 24, ...
- Multiples of 6: 6, 12, 18, 24, 30, ...

2. By observing the lists, we can see that 12 is the smallest number that is a multiple of all three numbers.

Therefore, Jenny, Mark, and Misty will all share dish duty again in 12 days.