The smallest 3 digit prime number is:

The smallest 3-digit number is 100, which is divisible by 2.

 100 is not a prime number.

101 < 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11.

√101 is a prime number.

Hence 101 is the smallest 3-digit prime number.