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