Question

Lauren goes to the park every 8 days, and Gloria goes to the park every 10 days.

a. They will meet at the park every 40 days.
b. They will meet at the park every 4 days.
c. They will never meet at the park.
d. They will meet at the park every 80 days.

Answer 1

Lauren and Gloria will meet at the park every 40 days, as 40 is the Least Common Multiple of their visit cycles (8 and 10 days respectively).

Step-by-step explanation:

To determine how often Lauren and Gloria meet at the park, we need to find the Least Common Multiple (LCM) of their visit cycles. Lauren goes every 8 days, and Gloria goes every 10 days. To find the LCM, we list the multiples of each number until we find a common multiple.

• Multiples of 8: 8, 16, 24, 32, 40, …
• Multiples of 10: 10, 20, 30, 40, …

The first common multiple of 8 and 10 is 40. Therefore, Lauren and Gloria will meet at the park every 40 days. So, the correct answer is (a) They will meet at the park every 40 days.