Question

A radio station plays yesterday by the beatles once every 2 days. Another station plays the same song once every 3 days. How many times in 30 days will both radio stations play the same song on the same day?

Answer 1

Both radio stations will play the same song on the same day 5 times in 30 days.

Explanation

A radio station plays yesterday by the Beatles once every 2 days. Another station plays the same song once every 3 days.

For finding the day on which both radio stations will play the same song, we will just find the LCM(Least Common Multiplier) of 2 and 3. So, the LCM will be 6.

That means, on every 6th day, both radio stations will play the same song.

So, the number of times that both radio stations will play the same song on the same day in 30 days $=(\frac{30}{6})= 5$