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