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