[newmathphys]

math/lcm.c has two defects in the same expression:

int lcm(int a, int b) { return (a * b) / gcd(a, b); }

1. The intermediate product overflows even when the answer does not

(a * b) is computed before the division. For a = b = 50000 the true lcm(50000, 50000) is 50000 - it fits in int with room to spare (about 40 000 times over) - but the intermediate product is 2500000000, which exceeds INT_MAX (2147483647). In C11 that is undefined behaviour, and the program prints a wrong answer:

$ gcc -w -O0 lib.c -o lcm_plain && ./lcm_plain 50000 50000
lcm(50000, 50000) = -35899          # should be 50000

$ gcc -w -O0 -fsanitize=undefined lib.c -o lcm_ubsan && ./lcm_ubsan 50000 50000
lib.c:19:35: runtime error: signed integer overflow: 50000 * 50000 cannot be
             represented in type 'int'
lcm(50000, 50000) = -35899

The file's own documented test cases (15,20 -> 60 and 12,18 -> 36) both stay far below sqrt(INT_MAX) ~ 46341, which is why this went unnoticed.

2. SIGFPE when both inputs are zero

gcd(0, 0) returns 0 (the a == 0 branch returns b), so the divisor is zero:

$ ./lcm_plain 0 0
Floating point exception (core dumped)   # exit code 136

lcm(0, 0) is conventionally 0.

The fix

int lcm(int a, int b)
{
    if (a == 0 || b == 0)
        return 0;

    return (a / gcd(a, b)) * b;
}

• Divide before multiplying. gcd(a, b) divides a exactly, so a / gcd(a, b) is exact and the intermediate value never exceeds the true LCM.
• Guard the zero case so gcd(0, 0) == 0 cannot become a divisor.

Verification after the patch

$ gcc -w -O0 -fsanitize=undefined lib_fixed.c -o lcm_fixed_bin
$ ./lcm_fixed_bin 50000 50000
lcm(50000, 50000) = 50000          # correct, no sanitizer diagnostic
$ ./lcm_fixed_bin 0 0
lcm(0, 0) = 0                      # no SIGFPE
$ ./lcm_fixed_bin 15 20
lcm(15, 20) = 60                   # unchanged
$ ./lcm_fixed_bin 12 18
lcm(12, 18) = 36                   # unchanged

Scope

The change is local to lcm(). gcd() is untouched. If lcm(a, b) itself does not fit in int, the result still cannot be represented - that is inherent in the int return type and is not claimed to be fixed here.

---

Found by stating a contract for the arithmetic and letting a solver refute it, then confirming with gcc.