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