Anita does laundry every other day. Every five days she changes sheets. Every 15 days she dusts. If she does all three chores today, how many days will it be before she does them all on the same day again?
30 days later. this is like least common multiples... 2, 5, 15. the least common multiple is 30.
Today is Day 1.
She does laundry on days 1, 3, 5, 7, 9, etc.
She changes sheets on days 1, 6, 11, 17, 21, 16, 31, etc.
She dusts on days 1, 16, 31, etc.
She changes sheets on days 1, 6, 11, 16, 21, 26, 31, etc
To find the number of days it will be before Anita does all three chores on the same day again, we need to find the least common multiple (LCM) of the numbers 2, 5, and 15.
First, let's list the multiples of each number until we find a common multiple:
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ...
Multiples of 5: 5, 10, 15, 20, ...
Multiples of 15: 15, 30, ...
From the lists above, we can see that the least common multiple (LCM) of 2, 5, and 15 is 30. Therefore, it will be 30 days before Anita does all three chores on the same day again.