Midterm Question 3

Question

Write a program that asks the user to enter two integers, then calculates and displays their greatest common divisor (GCD) and their Least common multiple (LCM).

寫一個輸入兩個整數 輸出它們的最大公因數程式

Hint: Use Euclidean Algorithm

使用歐幾里得演算法

LCM:

In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by LCM(a, b), is the smallest positive integer that is divisible by both a and b.

What is the LCM of 4 and 6?

Multiples of 4 are:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, ...

and the multiples of 6 are:

6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, ...

Common multiples of 4 and 6 are simply the numbers that are in both lists:

12, 24, 36, 48, 60, 72, ....

So, from this list of the first few common multiples of the numbers 4 and 6, their least common multiple is 12.

 

Example input: 

12 28

Example output (first number is GCD, second number is LCM):

4 84

 

Answer 1

Hidden content!
*   * * *****    *** *

int main(){

*  ** * ** ** * *  **   * ***     * a,b,i,max,min;

 * * ** * * ***   * * *    *   * ***** ** *  * *       **  *
*** **    **********   * *   *******  * && i<=b;i++){
 * *** *  ** * ****** **  ** *    ***  ****  ***   ***      && b%i==0)
** **   *   * * **    * *  * * ** ***   * * ** **  **** *** * *        * *  *** * **** * 
* *** * ** **  * **   **   
**    * *    **    ** ****** * *     * **  * ",max);

*  **   * ** * *** *** * *****   * *   **   *
      *   * ** ** ***** ***** ** ****   ** * **



return 0;
}

Comments

Case 0: Correct output
Case 1: Correct output
Case 2: Correct output
Case 3: Correct output
Case 4: Correct output

Answer 2

Hidden content!
#include<stdio.h>
int main()
{
   ** ** *** **   * * * *  a,b,c;
  *  ** * * * *  ** ** *  *   * *  *  *   *   *  ** ** * *  ** * 
  * *  *  ** **** *  **** **   ****   *
    {
** * * *  *   *  ** * ***   **  * *   **    ** **   *  *** 
   *  *  **    ***    *  *  **** **  * *         ****    ***
***      * *   **  ** *      *  * * **    *** *   
 ***  **** *  *      *    
*   * * * *   *    *  *  * *   *   * * ** *  
*  * ******  **   **   **     *  0;

}

Comments

Case 0: Wrong output
Case 1: Wrong output
Case 2: Wrong output
Case 3: Wrong output
Case 4: Wrong output

Answer 3

Hidden content!
#include   * **    * * ****
int main()
{
 **  ********** * *   *   *  **  n1, n2, i, gcd;

    *  **  * * *      * * * ****** * * ***   *  ******* &n1, &n2);

   ** ** ***** ***  * *  *** **  i <= n1 **  ** *  * **  i <= n2; ++i)
* *   * ** *      *  *   *  * 
 *** * *   ** *   * *    * *  *** *  * **  ** ** *   ** *   **    *** n2%i==0)
** ************     * * **** **  *  ** *    * *  ***  * *   = i;
* * *   **  *  **** ****  *
*** *  ** *    *  ** ** *   *  ***  ** ** **  * * *** gcd);
*** **  *  ***  ****   ******  * 0;
}

Comments

Case 0: Wrong output
Case 1: Wrong output
Case 2: Wrong output
Case 3: Wrong output
Case 4: Wrong output

Answer 4

Hidden content!
#include <stdio.h>
int main()
{
 * *     * *   ***   **** a,b,gcd,lcm;
***** * *      *** *  *****  * * * **  %d",&a,&b);
 ***** **** ** **  ******* * *  (a%b!=0)
  *  **** *  * * * ***  *  *  ****
* ****  * *** * *** ** ***   * * ****  *  *  * *       *  ***
*      *   *   ** ***     * **  **   *     *   ** **
 **  *  ** *** ****     ***    *  ** *  *  *   *  ****    
  * ** ** *  ** ** * ****
 * * *  **    ***  *  * **   ** **   *   *  *** *  *
 ***** *** *   **  ** ** **  * *  * %d",gcd,lcm);
*  ** * ** ***    *   **** * 0;
}

Comments

Case 0: Wrong output
Case 1: Wrong output
Case 2: Wrong output
Case 3: Wrong output
Case 4: Wrong output

Answer 5

Hidden content!
#include<stdio.h>
int main()
{
    ** ***  *  *** * **      * a,b,a1,b1,remainder,LCM;
*  **   * **   *   *****  ** ** ** %d",&a,&b);
*  **  * *    **      * * *  *
*** * * ***** **  * * *   *
** * *   **  *  *   *** **  *** ***
** *   *   ****  * ********  
**    **    **  *******  **      **** ***** ** **  *   *      **
**   **  *   * **  **** ** *     *  **   ***  *  * * ***** *  
 * *   *      ***    ** **     ******** *   **    *    ** * **
 **        **   *   *****  **  * 
*    ***   **** *      *  ********  **
*   * *  *** ******  **  *  *** * * * *** * %d",a,LCM);
* ** **   **********  ***  * * 0;
}

Comments

Case 0: Correct output
Case 1: Correct output
Case 2: Correct output
Case 3: Correct output
Case 4: Correct output

Answer 6

Hidden content!
#include <stdio.h>
int main()
{
    int a,b,i,x,y,gcd,lcm=0;
      **      *** *  *  **  * *     ** %d",&a,&b);
*   ** ***  *** * * *   * *  * **  ***  *  * *  
* *  ***   *     ** **  ***   * **** * * *  ***   ***  
  ****** *** ** *   *** **** *    ****  * **   *  *  * 
     ** ***  ** * ** ** **  **  ** **    *  * ** **  **  *   && y==0){
 *** *    * ** ** ***   * **     * * *** *     *** * *  **    **    * *** *    ** *   * ***  *   
***** **     *****     * *   ***** **** *        * *
    }
** * * *** ***         * ***  **  *
  ** *** *  **  *****    ***  
*  **** * * ****   *** *  *   ** ** *  *****   *  * * ** 
  **** *   ***** **  ** *     *** * *   *** ****   ** ***  **  ** **
       *   **** *     ******   * **** * *      *  * **        ** && y==0){
    **** * *    * * ****  ***   * ****   **** *****  * *  ** *** *  *  ** **  **
   *** ***     * **   * * *** ***   ***    * * *        ***  **  ****  * * ** *** *
 ****    **  * * * ***  * *  *  *    **  ***         *
* ** ***    *  ******  *** ** **   *****  ****  *   *  *
    }
   * ** * *  *  **  *  ***  *  * * * *** %d",gcd,lcm);
** ***    ** *  ****  * *   * * 0;
}

Comments

Case 0: Correct output
Case 1: Correct output
Case 2: Correct output
Case 3: Correct output
Case 4: Correct output