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