How to avoid overflow error when finding LCM for series of large integers

Question

I need to find least common divisor for a series of numbers (up to 100 000 numbers, each of them is in the range of [0, 2 000 000 000])

I am using the following algorithm lcm(a,b) = (a/gcd(a,b)) * b

The standard method of finding lcm for for than 2 numbers lcm(a, lcm(b,c))... is working for small input values.

However, for large input, it starts giving overflow error even if i used long long int...

How can I avoid having overflow error for many larger integer values?

Thank you for the help

Answer 1

Least common multiple in this case can be a large number with hundreds of digits. You need to handle such big integers.

gmplib library (-lgmp) supports arbitrary precision integer arithmetic:

int have_read_first_number = 0;
mpz_t result, arg;
mpz_inits(result, arg, NULL);
mpz_set_ui(arg, 1u);

/* read decimal integers from stdin: one per line */
while((len = getline(&token, &capacity, stdin)) > 0) {
  if (!have_read_first_number) { /* read the first integer */
    parse_mpz(token, result);
    have_read_first_number = 1; /* successfully read first integer */
  }
  else { /* read the rest of the numbers */
    parse_mpz(token, arg);
  }
  /* lcm(a, b, c, d) = lcm(lcm(lcm(a, b), c), d) */
  mpz_lcm(result, result, arg);
}
if (!have_read_first_number) /* error */
  panic("no numbers read");

/* print result as decimal */
mpz_out_str(stdout, 10, result);
puts("");

Example:

$ gcc lcm.c -o lcm -lgmp && { seq 1 100 | ./lcm; }
69720375229712477164533808935312303556800

Complete program: lcm.c