A warehouse manager is arranging delivery schedules for three suppliers. Supplier X delivers every 12 days, Supplier Y delivers every 18 days, and Supplier Z delivers every 30 days. All three suppliers made a delivery on the same day, which the manager marks as Day 0, and the manager wants to know on which future days their deliveries will align again, either for all three suppliers together or for just two of them at a time.

Separately, the manager is packing three different products into identical boxes for shipment. The manager has 84 units of Product A, 126 units of Product B, and 210 units of Product C, and wants to pack each product into boxes of the same size such that no units are left over in any product and the box size is as large as possible.

The manager has also noticed that a certain number, when divided by 12, 18, or 30, always leaves a remainder of 5 in every case, and wants to find the smallest such number that is still greater than 5.