Actually there are several. If you want the number exactly in between (which won't be an integer in this case), add the two numbers, and divide the result by two.
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13 is a prime number between 1 and 100. There are 24 others.
97 is the highest prime number between 1 and 100.
1 is the only number between 1 and 100 that has too few factors to be a prime number.
It is: 97
The common multiples of a number with itself are the multiples of that number. Thus all multiples of A between 1 and 100 are the common multiples of A and A between 1 and 100.