fix: Integer overflow of least_common_multiple. (#970)

* fix: Integer overflow of least_common_multiple.

* Update the typing (linter warning).

Author: fhlasek

math/least_common_multiple.cpp

@@ -26,12 +26,12 @@ unsigned int gcd(unsigned int x, unsigned int y) {
     if (x > y) {
         // The following is valid because we have checked whether y == 0
 
-        int temp = x / y;
+        unsigned int temp = x / y;
         return gcd(y, x - temp * y);
     }
     // Again the following is valid because we have checked whether x == 0
 
-    int temp = y / x;
+    unsigned int temp = y / x;
     return gcd(x, y - temp * x);
 }
 
@@ -40,7 +40,9 @@ unsigned int gcd(unsigned int x, unsigned int y) {
  * @params integer x and y whose lcm we want to find.
  * @return lcm of x and y using the relation x * y = gcd(x, y) * lcm(x, y)
  */
-unsigned int lcm(unsigned int x, unsigned int y) { return x * y / gcd(x, y); }
+unsigned int lcm(unsigned int x, unsigned int y) {
+  return x / gcd(x, y) * y;
+}
 
 /**
  * Function for testing the lcm() functions with some assert statements.
@@ -59,6 +61,15 @@ void tests() {
             lcm(2, 3) == 6));
     std::cout << "Second assertion passes: LCM of 2 and 3 is " << lcm(2, 3)
               << std::endl;
+
+    // Testing an integer overflow.
+    // The algorithm should work as long as the result fits into integer.
+    assert(((void)"LCM of 987654321 and 987654321 is 987654321 but lcm function"
+                  " gives a different result.\n",
+            lcm(987654321, 987654321) == 987654321));
+    std::cout << "Third assertion passes: LCM of 987654321 and 987654321 is "
+              << lcm(987654321, 987654321)
+              << std::endl;
 }
 
 /**