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No.356 Coincidence of Three Moving Points on a Circle

レベル : / AI推定難易度 : 1100 / 実行時間制限 : 1ケース 5.000秒 / メモリ制限 : 512 MB / 標準ジャッジ問題
タグ : （AC するまで非表示） / 解いたユーザー数 76
作問者 : 👑 tails
お気に入りにしたユーザー ProblemId : 616 / 自分の提出
問題文最終更新日: 2026-06-25 18:32:21
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Problem Statement

Three moving points $P_1, P_2, P_3$ are traveling clockwise around a circle of circumference $L$, each at a constant speed.
Point $P_1$ completes one lap of the circle in $T_1$ seconds.
Point $P_2$ completes one lap of the circle in $T_2$ seconds.
Point $P_3$ completes one lap of the circle in $T_3$ seconds.

Right now, the positions of all three moving points coincide.
How many seconds from now will the positions of all three moving points next coincide?
Give your answer as an irreducible fraction.

Input

$T_1$
$T_2$
$T_3$

$1 \le T_1 \lt T_2 \lt T_3 \le 10000$
$T_1, T_2, T_3$ are all integers.

Output

Output the number of seconds until the three moving points next coincide, as an irreducible fraction.
Following the sample output, print it in the format "numerator/denominator".

Sample

Sample 1
Input
2
3
4
Output
12/1

In 12 seconds, $P_1$ makes 6 laps, $P_2$ makes 4 laps, and $P_3$ makes 3 laps, returning to their original position.
During that time, the positions of the three moving points never coincide, so the answer is 12 seconds.
Even when the answer is an integer like this, do not omit the denominator from the output.

Sample 2
Input
15
21
35
Output
105/2

In 105/2 seconds, $P_1$ makes 3.5 laps, $P_2$ makes 2.5 laps, and $P_3$ makes 1.5 laps.

Sample 3
Input
40
52
130
Output
520/3

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