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It is impossible to list all the prime numbers: it has been proven (2000 years ago) that there are infinitely many. In other words, there is no last prime number.
The LCM of two numbers is the product of the numbers if one of the numbers is a prime. Since 11 is a prime, the LCM of 10 and 11 is 110 (10 x 11). If neither number had been a prime, the LCM would have been the product of all the prime factors of the numbers to their greatest power.
Prime numbers with hundreds of digits have been found, but there are still more to come that haven't been found yet. It's not possible to add up all the prime numbers, because nobody knows what they all are yet. Since there is no last prime number (this was proved 2000 years ago by Euclid), the sum of all prime numbers is infinite.
It has been proven that there is no largest prime number. You can find a list of the largest KNOWN prime numbers here: http://en.wikipedia.org/wiki/Largest_known_prime_number