Hi everyone!↵
↵
I recently came across this problem and I’m not sure how to approach it efficiently. Any hints or ideas would be appreciated!↵
↵
---↵
↵
## Problem Statement↵
↵
### Cyclic Divisibility↵
↵
Given three positive integers $a, b, c$, we need to find the smallest positive integer $x$ such that:↵
↵
$$↵
a \cdot x \equiv 0 \pmod b↵
$$↵
↵
$$↵
b \cdot x \equiv 0 \pmod c↵
$$↵
↵
$$↵
c \cdot x \equiv 0 \pmod a↵
$$↵
↵
---↵
## Input↵
↵
The first line contains an integer $T$ — the number of test cases ($1 \le T \le 10^5$).↵
↵
Each of the next $T$ lines contains three integers $a, b, c$ ($1 \le a, b, c \le 10^6$).↵
↵
---↵
↵
## Output↵
↵
For each test case, print a single integer — the minimum value of $x$ satisfying the conditions.↵
↵
---↵
↵
## Example↵
### Input↵
```↵
2↵
4 6 10↵
12 34 56↵
```↵
### Output↵
```↵
2↵
4 6 10↵
12 34 5630↵
1428↵
```↵
Thanks for reading! ↵
Any ideas or hints would be appreciated :)↵
↵
I recently came across this problem and I’m not sure how to approach it efficiently. Any hints or ideas would be appreciated!↵
↵
---↵
↵
## Problem Statement↵
↵
### Cyclic Divisibility↵
↵
Given three positive integers $a, b, c$, we need to find the smallest positive integer $x$ such that:↵
↵
$$↵
a \cdot x \equiv 0 \pmod b↵
$$↵
↵
$$↵
b \cdot x \equiv 0 \pmod c↵
$$↵
↵
$$↵
c \cdot x \equiv 0 \pmod a↵
$$↵
↵
---↵
## Input↵
↵
The first line contains an integer $T$ — the number of test cases ($1 \le T \le 10^5$).↵
↵
Each of the next $T$ lines contains three integers $a, b, c$ ($1 \le a, b, c \le 10^6$).↵
↵
---↵
↵
## Output↵
↵
For each test case, print a single integer — the minimum value of $x$ satisfying the conditions.↵
↵
---↵
↵
## Example↵
### Input↵
```↵
2↵
4 6 10↵
12 34 56↵
```↵
### Output↵
```↵
4 6 10↵
12 34 56
1428↵
```↵
Thanks for reading! ↵
Any ideas or hints would be appreciated :)↵
