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