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