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