The answer is 14 days.
To find when Laura and Kevin will operate on projects on the same day again, we need to find the least common multiple (LCM) of the intervals between their events.
Laura organizes an event every 2 days, and Kevin hosts an event per week (every 7 days).
The LCM of 2 and 7 will give us the number of days it takes for both of them to operate on projects on the same day again.
The prime factors of 2 are 2, and the prime factors of 7 are 7.
The LCM is calculated by taking the highest power of each prime factor that appears in either number:
LCM(2, 7) = 2^1 * 7^1 = 14
Therefore, it will take 14 days until Laura and Kevin operate on projects on the same day again.