{"trustable":true,"sections":[{"title":"","value":{"format":"MD","content":"**LCM** is an abbreviation used for **L**east **C**ommon **M**ultiple in Mathematics. We say **LCM (a, b, c) \u003d L** if and only if **L** is the least integer which is divisible by **a, b** and **c**.\n\nYou will be given **a, b** and **L**. You have to find **c** such that **LCM (a, b, c) \u003d L**. If there are several solutions, print the one where **c** is as small as possible. If there is no solution, report so."}},{"title":"Input","value":{"format":"MD","content":"Input starts with an integer **T (\u0026#8804; 325)**, denoting the number of test cases.\n\nEach case starts with a line containing three integers **a** **b L (1 \u0026#8804; a, b \u0026#8804; 10\u003csup\u003e6\u003c/sup\u003e, 1 \u0026#8804; L \u0026#8804; 10\u003csup\u003e12\u003c/sup\u003e)**."}},{"title":"Output","value":{"format":"MD","content":"For each case, print the case number and the minimum possible value of **c**. If no solution is found, print `impossible`."}},{"title":"Sample","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e3\n3 5 30\n209475 6992 77086800\n2 6 10\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eCase 1: 2\nCase 2: 1\nCase 3: impossible\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}