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