Problem SOLUTION CODECHEF
Alice and Bob are playing a game. They have two positive integers � and �
In one operation:
- First Alice would replace exactly one of the numbers with the gcd of current numbers. In words, she would select either � or � and replace it with gcd(�,�).
- Then Bob would replace exactly one of the numbers with the lcm of current numbers.
Find the minimum sum of numbers they can achieve after � number of operations.
- The first line of input will contain a single integer �, denoting the number of test cases.
- Each test case consists of three space-separated integers �,�, and � — denoting the initial numbers and the number of operations.
For each test case, output on a new line, the minimum sum of numbers they can achieve after � operations.
3 4 2 1 1 5 2 4 4 10
4 2 8
Test case 1: Alice will replace 4 by the gcd, which is 2. The numbers become 2 and 2. Then, Bob will replace 2 with the lcm, which is 2. Thus, the final sum is 4.
Test case 3: Since both numbers are equal, both gcd and lcm would be 4. Thus, the sum of two numbers after all operations remains same, i.e., 8.