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