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