Every 2 days Andy takes out the trash. Every 3 day he sweeps the kitchen. what is the least number of days that will pass before Andy will have to do both chores together on the same days?

The least number of days that will pass before Andy will have to do both chores together on the same days are 5 days.

Step-by-step explanation:

Let us start from the initial day.

Every 2 days Andy takes out the trash.

So, the days he takes out trash are second day, fourth day, sixth day, eighth day, tenth day and so on ... (1)

Every 3 days Andy sweeps the kitchen.

So, the days he sweeps the kitchen are third day, sixth day, ninth day, twelfth day and so on ... (2)

Now, on comparing both equations (1) and (2) we see the first common day to both the chores is SIXTH DAY.

Hence, the least number of days that will pass before Andy will have to do both chores together on the same days are 5 days.