feat: Added a function for finding the least common multiple (#840)

* feat: Added a function for finding the least common multiple

* feat: Miller-Rabin Primality Test (probabilistic)

* Added test assertions

* Mistakenly worked on a different branch

* Doxygen comments

* Comments changed

math/least_common_multiple.cpp

@@ -0,0 +1,70 @@
+/**
+ * Copyright 2020 @author tjgurwara99
+ * @file
+ *
+ * A basic implementation of LCM function
+ */
+
+#include <cassert>
+#include <iostream>
+
+/**
+ * Function for finding greatest common divisor of two numbers.
+ * @params two integers x and y whose gcd we want to find.
+ * @return greatest common divisor of x and y.
+ */
+unsigned int gcd(unsigned int x, unsigned int y) {
+    if (x == 0) {
+        return y;
+    }
+    if (y == 0) {
+        return x;
+    }
+    if (x == y) {
+        return x;
+    }
+    if (x > y) {
+        // The following is valid because we have checked whether y == 0
+
+        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;
+    return gcd(x, y - temp * x);
+}
+
+/**
+ * Function for finding the least common multiple of two numbers.
+ * @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); }
+
+/**
+ * Function for testing the lcm() functions with some assert statements.
+ */
+void tests() {
+    // First test on lcm(5,10) == 10
+    assert(((void)"LCM of 5 and 10 is 10 but lcm function gives a different "
+                  "result.\n",
+            lcm(5, 10) == 10));
+    std::cout << "First assertion passes: LCM of 5 and 10 is " << lcm(5, 10)
+              << std::endl;
+
+    // Second test on lcm(2,3) == 6 as 2 and 3 are coprime (prime in fact)
+    assert(((void)"LCM of 2 and 3 is 6 but lcm function gives a different "
+                  "result.\n",
+            lcm(2, 3) == 6));
+    std::cout << "Second assertion passes: LCM of 2 and 3 is " << lcm(2, 3)
+              << std::endl;
+}
+
+/**
+ * Main function
+ */
+int main() {
+    tests();
+    return 0;
+}