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