P10570 [JRKSJ R8] Tennis.

~~Baseball is orange~~ Tennis is green. ~~Tennis is rising, tennis is falling~~. > And you never meet the people, you never shake their hands, you never hear their story or tell yours. > But somehow in the act of making something with a great deal of care and love, something's transmitted there.

You have two gears meshed together. You want that every time gear A rotates $a$ turns, gear B rotates exactly $b$ turns. Because of precision requirements, each gear must have **at least** $c$ teeth. Find the minimum possible value of the sum of the numbers of teeth of gear A and gear B.

**This problem has multiple test cases.** The first line contains an integer $T$ describing the number of test cases. For each test case: - One line with three integers $a, b, c$.

For each test case, output one integer per line, representing the answer.

### Sample Explanation - For the first test case, the optimal solution is that gear A has $6$ teeth and gear B has $4$ teeth, so the answer is $4 + 6 = 10$. - For the second test case, the optimal solution is that gear A has $10$ teeth and gear B has $5$ teeth, so the answer is $10 + 5 = 15$. - For the third test case, the optimal solution is that gear A has $8$ teeth and gear B has $20$ teeth, so the answer is $8 + 20 = 28$. ### Constraints and Notes **This problem uses bundled testdata.** Let $v = \max(a, b, c)$. - Subtask 0 (13 pts): $v \leq 20$. - Subtask 1 (13 pts): $v \leq 5000$. - Subtask 2 (20 pts): $v \leq 10^6$. - Subtask 3 (54 pts): No special restrictions. For all testdata, it is guaranteed that $1 \leq T \leq 8\times 10^3$ and $1 \leq a, b, c \leq 10^9$. # Input Format # Output Format Translated by ChatGPT 5