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