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