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