# Task for Alexey Codechef Solution|Problem Code: ALEXTASK

## Problem

Alexey is trying to develop a program for a very simple microcontroller. It makes readings from various sensors over time, and these readings must happen at specific regular times. Unfortunately, if two of these readings occur at the same time, the microcontroller freezes and must be reset.

There areÂ NÂ different sensors that read data on a regular basis. For eachÂ iÂ fromÂ 1Â toÂ N, the reading from sensorÂ iÂ will occur everyÂ AiÂ milliseconds with the first reading occurring exactlyÂ AiÂ milliseconds after the microcontroller is powered up. Each reading takes precisely one millisecond on Alexeyâ€™s microcontroller.

Alexey wants to know when the microcontroller will freeze after he turns it on.

### Input

The first line of the input contains an integerÂ TÂ denoting the number of test cases. The description ofÂ TÂ test cases follows.

The first line contains single integerÂ NÂ denoting the number of sensors.

The second line containsÂ NÂ space-separated integersÂ A1, A2, â€¦, ANÂ denoting frequency of measurements. Namely, sensorÂ iÂ will be read everyÂ AiÂ milliseconds with the first reading occurringÂ AiÂ milliseconds after the microcontroller is first turned on.

### Output

For each test case, output a single line containing the number of milliseconds until the microcontroller freezes.

### Constraints

• 1Â â‰¤Â TÂ â‰¤Â 10
• 2Â â‰¤Â NÂ â‰¤Â 500
• 1Â â‰¤Â AiÂ â‰¤Â 109

Subtask #1 (10 points)Â 1Â â‰¤Â TÂ â‰¤Â 10,2Â â‰¤Â NÂ â‰¤Â 9,Â 1Â â‰¤Â AiÂ â‰¤Â 500Subtask #2 (20 points)Â 1Â â‰¤Â TÂ â‰¤Â 10,2Â â‰¤Â NÂ â‰¤Â 500,1Â â‰¤Â AiÂ â‰¤Â 1000Subtask #3 (70 points)Â original constraints

3
3
2 3 5
4
1 8 7 11
4
4 4 5 6

6
7
4

### Explanation

Case 1: in 6 milliseconds, the third reading will be attempted from the 1st sensor and the second reading will be attempted from the 2nd sensor.

Case 2: in 7 milliseconds the seventh reading will be attempted from the 1st sensor and the first reading will be attempted from the 3rd sensor.

Case 3: in 4 milliseconds, the first readings from the first two sensors will be attempted.

## Task for Alexey â€“ CodeChef Solution in JAVA

import java.util.Scanner;
public class Main {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int T = sc.nextInt();
for (int tc = 0; tc < T; tc++) {
int N = sc.nextInt();
int[] A = new int[N];
for (int i = 0; i < A.length; i++) {
A[i] = sc.nextInt();
}
System.out.println(solve(A));
}
sc.close();
}
static long solve(int[] A) {
long result = Long.MAX_VALUE;
for (int i = 0; i < A.length; i++) {
for (int j = i + 1; j < A.length; j++) {
result = Math.min(result, lcm(A[i], A[j]));
}
}
return result;
}
static long lcm(int a, int b) {
return (long) a / gcd(a, b) * b;
}
static int gcd(int a, int b) {
return (b == 0) ? a : gcd(b, a % b);
}
}

Disclaimer:Â The above Problem (Task for Alexey) is generated byÂ CodeChef but the solution is provided byÂ Chase2learn.This tutorial is only forÂ EducationalÂ andÂ LearningÂ purpose.

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