[C language] Input two positive integers m and n, and find their greatest common divisor and least common multiple. (required to be implemented with a while statement)

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One, the greatest common divisor method

(1) tossing and dividing method

There are two integers a and b:
① a%b is the remainder c
② If c==0, then b is the greatest common divisor of the two numbers
③ If c! =0, then a=b, b=c, and then go back to execute ①.

For example, the process of finding the greatest common divisor of 27 and 15 is:
27÷15 remainder 12
15÷12 remainder 3
12÷3 remainder 0
Therefore, 3 is the greatest common divisor.

(2) Subtraction

There are two integers a and b:
① If a>b, then a=ab
② If a<b, then b=ba
③ If a==b, then a (or b) is the greatest common divisor of the two
numbers④ If a! =b, then go back and execute ①.

For example, the process of finding the greatest common divisor of 27 and 15 is:
27-15=12( 15>12 )
15-12=3( 12>3 )
12-3=9( 9>3 )
9-3=6( 6> 3)
6-3=3 (3==3)
Therefore, 3 is the greatest common divisor.

Second, find the least common multiple algorithm

Least common multiple = product of two integers ÷ greatest common divisor

code show as below:

#include <stdio.h>
int main()
{
    
    
    int m,n,max,min,b,c;
	printf("请输入两个整数：\n");
	scanf("%d%d",&m,&n);
    c=m%n;
    b=m*n;
	while(c!=0)
	{
    
    
        m=n;
		n=c;
        c=m%n;
	}
    max=n;
	min=b/max;
	printf("\n最大公约数为：%d\n最小公倍数为：%d\n",max,min);
    return 0;
}

Output result: