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