Question

Today, the cricket team, the soccer team and the basketball team, all had games. The cricket team plays every 2nd day, the soccer team plays every 3rd day and the basketball team plays every 5th day. On which of the following day from today, will all the teams have games on the same day again?

• A. ${18}^{th}$
• B. ${10}^{th}$
• C. ${30}^{th}$
• D. ${15}^{th}$

Answer 1

The correct option is C ${30}^{th}$

To find when all teams have games on the same day again, we need to find the the common multiples of the days after which team has a game.

Multiples of 2:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32

Multiples of 3:
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33

Multiples of 5:
5, 10, 15, 20, 25, 30, 35

We can see that, 30 is a common multiple of 2, 3 and 5.
Hence, 30th day from today, all the teams will have games on the same day again.