求最大公约数和最小共倍数的方法（除穷举）

#include<bits/stdc++.h>
using namespace std;
int main(){//  辗转相除法求最大公约数 
    int a,b,c;
    scanf("%d%d",&a,&b);
    int m=a,n=b;
    while(c!=0){// 余数不为0，继续相除，直到余数为0 
        c=a%b;
        a=b;
        b=c;
    }
    printf("The largest common divisor:%d\n",a);//注意这里不是b，因为跳出循环时b已经是c了
    printf("The least common multiple:%d",m*n/a);
    return 0;
}

#include<bits/stdc++.h>
using namespace std;
int a,b;
int main(){
    scanf("%d%d",&a,&b);
    int m=a,n=b;
    while(a!=b){
        if(a>b)a=a-b;
        if(a<b)b=b-a;
    }
    printf("The largest common divisor:%d\n",a);
    printf("The least common multiple:%d",m*n/a);
    return 0;
}

#include<bits/stdc++.h>
using namespace std;
int x,y;
int ans;
int gcd(int a,int b){//求最大公约数
    //if(a<b)swap(a,b);
    if(a%b==0)return b;
    if(a==b)return b;
    return gcd(b,a%b);
}

int lcm(int a,int b){//求最小共倍数
    return a*b/gcd(a,b);
}

int main(){
    scanf("%d%d",&x,&y);
    for(int i=x;i<=y;i++){
        int j=x*y/i;
        if(gcd(i,j)==x&&lcm(i,j)==y){
            ans++;
        }
    }
    printf("%d",ans);
    return 0;
}