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