# The product mystery - Codechef

### Problem Statement :

```Given two positive numbers B and C, what is the minimum positive value of A, such that A⋅B is divisible by C.

Here, A⋅B denotes the value obtained when A is multiplied by B.

Input Format

The first line will contain an integer T - number of test cases. Then the test cases follow.
The first and only line of each test case contains two integers B and C.

Output Format

For each test case, output the minimum value of A such that A⋅B is divisible by C.

Constraints

1≤T≤105
1≤B,C≤109

Sample Input 1

2
2 4
8 12

Sample Output 1
2
3```

### Solution :

```                        ```Solution in C++ :

#include<bits/stdc++.h>
#include <iterator>
#include <iostream>
#include <numeric>
#include <math.h>
#define ll long long
#define ull long
#define mpa make_pair
#define pb push_back
#define ff first
#define pii pair<ll,ll>
#define dd long double
#define trace(x) cerr << #x << " : " << x << endl
#define ss second
#define boost ios_base::sync_with_stdio(0)
#define forp(i,a,b) for(ll i=a;i<=b;i++)
#define rep(i,n)    for(ll i=0;i<n;++i)
#define ren(i,n)    for(ll i=n-1;i>=0;i--)
#define forn(i,a,b) for(ll i=a;i>=b;i--)
#define all(c) (c).begin(),(c).end()
#define tr(c,i) for(typeof((c).begin()) i = (c).begin(); i != (c).end();
#define sc(x) scanf("%lld",&x)
#define clr(x,val) memset(x,val,sizeof(x))
#define pr(x) printf("%lld\n",x)
#define gc getchar
#define pdd pair<dd,dd>
#define prec(x) cout<<fixed<<setprecision(x)
#define fre freopen("input.txt","r",stdin),freopen("output.txt","w",stdout)
#define arr array
using namespace std;
ll a[200005];
void solve(ll tc){
ll b,c;
cin>>b>>c;
ll gc=__gcd(b,c);
cout<<c/gc<<endl;

}

int main(){
boost;

//pre_cum();
//prec(20);
//fre;

ll t=1;
ll tc=1;
cin>>t;

while(t--){
solve(tc);
tc++;
}

return 0;

}```
```

```                        ```Solution in Java :

import java.util.*;
import java.io.*;

public class Main {

static long startTime = System.currentTimeMillis();

// for global initializations and methods starts here

// global initialisations and methods end here

static void run() {
boolean tc = true;

try (OutputStream out = new BufferedOutputStream(System.out)) {

//long startTime = System.currentTimeMillis();

int testcases = tc ? r.ni() : 1;
int tcCounter = 1;
// Hold Here Sparky------------------->>>
// Solution Starts Here

start:
while (testcases-- > 0) {

// a*b = c

long b = r.nl();
long c = r.nl();

out.write((c / gcd(b, c) + " ").getBytes());
out.write(("\n").getBytes());
}
// Solution Ends Here
} catch (IOException e) {
e.printStackTrace();
}
}

static class AdityaFastIO {
final private int BUFFER_SIZE = 1 << 16;
private final DataInputStream din;
private final byte[] buffer;
private int bufferPointer, bytesRead;
public StringTokenizer st;

din = new DataInputStream(System.in);
buffer = new byte[BUFFER_SIZE];
bufferPointer = bytesRead = 0;
}

public AdityaFastIO(String file_name) throws IOException {
din = new DataInputStream(new FileInputStream(file_name));
buffer = new byte[BUFFER_SIZE];
bufferPointer = bytesRead = 0;
}

public String word() {
while (st == null || !st.hasMoreElements()) {
try {
st = new StringTokenizer(br.readLine());
} catch (IOException e) {
e.printStackTrace();
}
}
return st.nextToken();
}

public String line() {
String str = "";
try {
} catch (IOException e) {
e.printStackTrace();
}
return str;
}

public String readLine() throws IOException {
byte[] buf = new byte[100000001]; // line length
int cnt = 0, c;
while ((c = read()) != -1) {
if (c == '\n') break;
buf[cnt++] = (byte) c;
}
return new String(buf, 0, cnt);
}

public int ni() throws IOException {
int ret = 0;
byte c = read();
while (c <= ' ') c = read();
boolean neg = (c == '-');
if (neg) c = read();
do {
ret = ret * 10 + c - '0';
}
while ((c = read()) >= '0' && c <= '9');
if (neg) return -ret;
return ret;
}

public long nl() throws IOException {
long ret = 0;
byte c = read();
while (c <= ' ') c = read();
boolean neg = (c == '-');
if (neg) c = read();
do {
ret = ret * 10 + c - '0';
}
while ((c = read()) >= '0' && c <= '9');
if (neg) return -ret;
return ret;
}

public double nd() throws IOException {
double ret = 0, div = 1;
byte c = read();
while (c <= ' ') c = read();
boolean neg = (c == '-');
if (neg) c = read();
do {
ret = ret * 10 + c - '0';
}
while ((c = read()) >= '0' && c <= '9');
if (c == '.') while ((c = read()) >= '0' && c <= '9') ret += (c - '0') / (div *= 10);
if (neg) return -ret;
return ret;
}

private void fillBuffer() throws IOException {
bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
if (bytesRead == -1) buffer[0] = -1;
}

private byte read() throws IOException {
if (bufferPointer == bytesRead) fillBuffer();
return buffer[bufferPointer++];
}

public void close() throws IOException {
if (din == null) return;
din.close();
}
}

public static void main(String[] args) throws Exception {
run();
}

static int[] readIntArr(int n, AdityaFastIO r) throws IOException {
int[] arr = new int[n];
for (int i = 0; i < n; i++) arr[i] = r.ni();
return arr;
}

static long[] readLongArr(int n, AdityaFastIO r) throws IOException {
long[] arr = new long[n];
for (int i = 0; i < n; i++) arr[i] = r.nl();
return arr;
}

static List<Integer> readIntList(int n, AdityaFastIO r) throws IOException {
List<Integer> al = new ArrayList<>();
for (int i = 0; i < n; i++) al.add(r.ni());
return al;
}

static List<Long> readLongList(int n, AdityaFastIO r) throws IOException {
List<Long> al = new ArrayList<>();
for (int i = 0; i < n; i++) al.add(r.nl());
return al;
}

static long mod = 998244353;

static long modInv(long base, long e) {
long result = 1;
base %= mod;
while (e > 0) {
if ((e & 1) > 0) result = result * base % mod;
base = base * base % mod;
e >>= 1;
}
return result;
}

static class FastReader {
StringTokenizer st;

}

String word() {
while (st == null || !st.hasMoreElements()) {
try {
st = new StringTokenizer(br.readLine());
} catch (IOException e) {
e.printStackTrace();
}
}
return st.nextToken();
}

String line() {
String str = "";
try {
} catch (IOException e) {
e.printStackTrace();
}
return str;
}

int ni() {
return Integer.parseInt(word());
}

long nl() {
return Long.parseLong(word());
}

double nd() {
return Double.parseDouble(word());
}
}

static int MOD = (int) (1e9 + 7);

static long powerLL(long x, long n) {
long result = 1;
while (n > 0) {
if (n % 2 == 1) result = result * x % MOD;
n = n / 2;
x = x * x % MOD;
}
return result;
}

static long powerStrings(int i1, int i2) {
String sa = String.valueOf(i1);
String sb = String.valueOf(i2);
long a = 0, b = 0;
for (int i = 0; i < sa.length(); i++) a = (a * 10 + (sa.charAt(i) - '0')) % MOD;
for (int i = 0; i < sb.length(); i++) b = (b * 10 + (sb.charAt(i) - '0')) % (MOD - 1);
return powerLL(a, b);
}

static long gcd(long a, long b) {
if (a == 0) return b;
else return gcd(b % a, a);
}

static long lcm(long a, long b) {
return (a * b) / gcd(a, b);
}

static long lower_bound(int[] arr, int x) {
int l = -1, r = arr.length;
while (l + 1 < r) {
int m = (l + r) >>> 1;
if (arr[m] >= x) r = m;
else l = m;
}
return r;
}

static int upper_bound(int[] arr, int x) {
int l = -1, r = arr.length;
while (l + 1 < r) {
int m = (l + r) >>> 1;
if (arr[m] <= x) l = m;
else r = m;
}
return l + 1;
}

static void addEdge(ArrayList<ArrayList<Integer>> graph, int edge1, int edge2) {
}

public static class Pair implements Comparable<Pair> {
int first;
int second;

public Pair(int first, int second) {
this.first = first;
this.second = second;
}

public String toString() {
return "(" + first + "," + second + ")";
}

public int compareTo(Pair o) {
// TODO Auto-generated method stub
if (this.first != o.first)
return (int) (this.first - o.first);
else return (int) (this.second - o.second);
}
}

public static class PairC<X, Y> implements Comparable<PairC> {
X first;
Y second;

public PairC(X first, Y second) {
this.first = first;
this.second = second;
}

public String toString() {
return "(" + first + "," + second + ")";
}

public int compareTo(PairC o) {
// TODO Auto-generated method stub
return o.compareTo((PairC) first);
}
}

static boolean isCollectionsSorted(List<Long> list) {
if (list.size() == 0 || list.size() == 1) return true;
for (int i = 1; i < list.size(); i++) if (list.get(i) <= list.get(i - 1)) return false;
return true;
}

static boolean isCollectionsSortedReverseOrder(List<Long> list) {
if (list.size() == 0 || list.size() == 1) return true;
for (int i = 1; i < list.size(); i++) if (list.get(i) >= list.get(i - 1)) return false;
return true;
}

}```
```

```                        ```Solution in Python :

import math
for _ in range(int(input())):
b, c = map(int, input().split())
print(c // math.gcd(b, c))```
```

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