Danny binge watches four TV shows. His viewing habits include:

One show every other day

Another show every 3rd day

Another show every 5th day

Last show every 10th day

If Danny watched all four shows on August 1, when will he watch all of them on the same day again?

Danny will watch all of them on the same day again on August 31

Step-by-step explanation:

Here, we have a word problem.

The shows and frequency of watching are;

Show A Every 2 days

Show B Every 3rd day

Show C Every 5th day

Show D Every 10th day

Danny watched all four shows on August 1, therefore, the day he will watch all four shows can be found by finding the Lowest Common Multiple, LCM of the frequency of his watching each of the shows. That is, the LCM of 2, 3, 5 and 10

Therefore we have, since 10 is the highest frequency and 3 is not a factor of 10, then the LCM that applies to 3 and 10 is 3*10 = 30.

Since the other frequencies are also a factor of 30, then the LCM of 2, 3, 5, and 10 is 30

Therefore, Danny will watch all four shows again on the same day again in 30 days after August 1. That is August (1 + 30) = August 31.