Min Max LCM CodeChef SnackDown 2021 Round 1A Solution

Question

You are given two positive integers X and K.

You have to output the minimum and maximum value of LCM(i,j) where X≤i<j≤X⋅K.

We define LCM(i,j) for two positive integers i and j as the minimum positive integer y such that both i and j divide y without remainder.

Input Format

First line will contain T, number of testcases. Then the testcases follow.

Each testcase contains of a single line of input, two space separated integers X and K.

Output Format

For each testcase, output two space separated integers - the minimum and maximum possible value respectively of LCM(i,j) where X≤i<j≤X⋅K.

Constraints

1≤T≤10^5

1≤X≤10^8

2≤K≤10^8

It is guaranteed that, for each test case, X⋅K≤10^9

Sample Input 1 

2

4 3

2 3

Sample Output 1 

8 132

4 30

Explanation

Test Case 1: We want to find the minimum and maximum value of LCM(i,j) for 4≤i<j≤12. It is easy to verify that the LCM(4,8)=8 is the minimum possible value whereas LCM(11,12)=132 is the maximum value.

Test Case 2: We want to find the minimum and maximum value of LCM(i,j) for 2≤i<j≤6. The maximum value is obtained for the pair (5,6) whereas the minimum is obtained for the pair (2,4).

Program Code in C++

#include <bits/stdc++.h>

#define ll long long int

using namespace std;

int main() {

ll t;

cin>>t;

while(t--){

    ll x,y;

    cin>>x>>y;

    cout<<x*2<<" "<<((x*y)-1)*(x*y)<<endl;

}

return 0;

}

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