Question

people are waiting in line for a theatre premiere every 5th person in line will receive a free theater ticket every 6th person will receive a gift card for $40 which person is the first to receive both prizes

Answer 1

List out the multiples of each number (5 and 6). I'm going to list out ten multiples of each.

5, 10, 15, 20, 25, 30, 35, 40, 45, 50, ...

6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...

Note how 30 is the smallest number that shows in both lists. So the lowest common multiple (LCM) of 5 and 6 is 30

As a shortcut, you can multiply 5 and 6 to get 30. This trick only works if there are no other common factors between 5 and 6 (factors other than 1)

Answer: The 30th person will be the first person to get both prizes.