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