Question

Zeke has swim club every 2 days and robotics club every 8 days. He claims the first day he'll have both clubs on the same day is the 16th day of the month due to the LCM of 2 and 8 being 16. Does Zeke's reasoning make sense?

Answer 1

Zeke's claim is incorrect; the LCM of 2 and 8 is 8, meaning that he will have both clubs on the same day every 8 days, not on the 16th day.

Step-by-step explanation:

No, Zeke's reasoning does not make sense because the Least Common Multiple (LCM) of 2 and 8 is not 16. The LCM of two numbers is the smallest number that is a multiple of both numbers. To find the LCM of 2 and 8, we list the multiples of each number until we find a common multiple:

• Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ...
• Multiples of 8: 8, 16, 24, 32, 40, ...

The smallest multiple that both lists share is 8. Therefore, the LCM of 2 and 8 is 8, not 16. This means that Zeke will have both clubs on the same day every 8 days, not on the 16th day as he claimed.