1. Kolya, Seryozha, and Vanya regularly go to the cinema: Kolya goes there every 4th day, Seryozha - every 5th day, and Vanya - every 6th day. Today all the boys were at the cinema. When will all three meet at the cinema again?
1. Answer: 60.

Let's start numbering the days beginning with tomorrow (today's day is "zero"). Kolya will go to the cinema on the days whose numbers are divisible by 4, Seryozha - on the days whose numbers are divisible by 5, Vanya - on the days whose numbers are divisible by 6. For them to all be at the cinema together, the day number must be divisible by 4, 5, and 6. This will first happen on the day with the number $\operatorname{LCM}(4,5,6)=60$