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