求2个及多个正整数的最大公约数和最小公倍数的三种方法

package com.wener;
/**
 * 使用辗转相除法求
 */
import java.util.Scanner;

public class HomeWork01 {	
	    public static void main(String[]args){
	        Scanner scan = new Scanner(System.in);
	        System.out.print("请输入第一个整数:\n");
	        int a = scan.nextInt();
	        System.out.print("请输入第二个整数:\n");
	        int b = scan.nextInt();
	        if(a>0&&b>0) {
	        Max_Min(a,b);
	        }else {
	        	System.out.println("请输入两个正整数！");
	        }
	    }
	    public static void Max_Min(int a,int b){
	        int i = a;
	        int j = b;
	        int x =0,y =0;
	        if(a < b){
	            x = b;
	            b = a;
	            a = x;
	        }
	        while(b != 0){
	            y = a % b;
	            a = b;
	            b = y;
	        }
	        //最小公倍数
	        int t = i * j / a;
	        System.out.println(i+"和"+j+"的最大公约数为："+ a);
	        System.out.println(i+"和"+j+"的最小公倍数为："+ t);  
	    }
	}




package com.wener;
/**
 * 使用相减法求
 */
import java.util.Scanner;

public class HomeWork02 {
	public static void main(String[]args) {
		int z=0;
		Scanner scan = new Scanner(System.in);
        System.out.print("请输入第一个整数:\n");
        int x = scan.nextInt();
        System.out.print("请输入第二个整数:\n");
        int y = scan.nextInt();
        if(x>0&&y>0) {
        z=Subtraction(x,y);
        System.out.println("最大公约数为 : "+z);
		System.out.println("最小公倍数为: "+(x*y/z));
        }else {
        	System.out.println("请输入两个正整数！");
        }
	}
	public static int Subtraction(int x,int y){
		while(x!=y){
			if(x>y){
				x=x-y;
			}
			else{
				y=y-x;
			}
		}
		return x;
	}
}

package com.wener;
/**
 * 使用穷举法求
 */
import java.util.Scanner;

public class HomeWork03 {
		public static void main(String[]args) {
			int z=0;
			Scanner scan = new Scanner(System.in);
	        System.out.print("请输入第一个整数:\n");
	        int x = scan.nextInt();
	        System.out.print("请输入第二个整数:\n");
	        int y = scan.nextInt();
	        if(x>0&&y>0) {
	        z = divisor(x,y);
	        z = multiple(x,y);
	        System.out.println("最大公约数为 : "+divisor(x,y));
			System.out.println("最小公倍数为: "+multiple(x,y));
	        }else {
	        	System.out.println("请输入两个正整数！");
	        }
		}
		public static int divisor(int x,int y){
			int z;
			for(z=x;z>0;z--){
				if(x%z==0&&y%z==0){
					break;
				}
			}
			return z;
		}
		public static int multiple(int x,int y){
			int z;
			for(z=x;;z++){
				if(z%x==0&&z%y==0){
					break;
				}
			}
			return z;
		}
}

package com.wener;

import java.util.Scanner;

/*
 * 求多个正整数的最大公约数和最小公倍数
 */
public class HomeWork04 {
		public static void main(String[] args) {
			Scanner sc=new Scanner(System.in);
			System.out.println("请输入第一个数:");
			int a=sc.nextInt();
			System.out.println("请输入第二个数:");
			int b=sc.nextInt();
			System.out.println("请输入数的个数并且和每个数:");//n为数组的个数
			int n=sc.nextInt();
			int[] num=new int[n];
			for(int i=0;i<n;i++) {
				num[i]=sc.nextInt();
			}
			System.out.println(n+"个数的最大公约数为"+getMoreBigDiv(num, n));

			System.out.println(n+"个数的最小公倍数"+getMoreSmallMul(num, n));
		}

		public static int getBigDiv(int a, int b) {// 求两个数的最大公约数
		if (b == 0)
		return a;
		return getBigDiv(b, a % b);
		}


		public static int getSmallMul(int a, int b) {// 求两个数的最小公倍数
		return (a * b) / getBigDiv(a, b);
		}


		public static int getMoreBigDiv(int num[], int n) { // 求多个数的最大公约数
		if (n == 1)
		return num[n - 1];
		return getBigDiv(num[n - 1], getMoreBigDiv(num, n - 1));
		}


		public static int getMoreSmallMul(int num[], int n) {// 求多个数的最小公倍数
		if (n == 1)
		return num[n - 1];
		return getSmallMul(num[n - 1], getMoreSmallMul(num, n - 1));
		}
		}