Find the smallest positive integer that is greater than $1$ and relatively prime to the product of the first 20 positive integers. Reminder: two numbers are relatively prime if their greatest common divisor is 1.

23

Step-by-step explanation:

since the number is relatively prime to the product of the first 20 positive numbers

It number must not have factor of (1-20)

Therefore the smallest possible number is the next prime after 20

Answer is 23

72 is the answer to this problem