實作歐幾裡得演算法來找出兩個整數的最大公約數(GCD) 和最小公倍數(LCM),並將結果與給定整數一起輸出。
實作歐幾裡得演算法求兩個整數的最大公約數(GCD) 與最小公倍數(LCM) 的解如下-
求GCD和LCM 的邏輯如下-if(firstno*secondno!=0){ gcd=gcd_rec(firstno,secondno); printf("</p><p>The GCD of %d and %d is %d</p><p>",firstno,secondno,gcd); printf("</p><p>The LCM of %d and %d is %d</p><p>",firstno,secondno,(firstno*secondno)/gcd); }
調用的函數如下-
int gcd_rec(int x, int y){ if (y == 0) return x; return gcd_rec(y, x % y); }
以下是C 程序,用於實現歐幾里德演算法,以求兩個整數的最大公約數(GCD) 和最小公倍數(LCM) -< /p>
現場示範
#include<stdio.h> int gcd_rec(int,int); void main(){ int firstno,secondno,gcd; printf("Enter the two no.s to find GCD and LCM:"); scanf("%d%d",&firstno,&secondno); if(firstno*secondno!=0){ gcd=gcd_rec(firstno,secondno); printf("</p><p>The GCD of %d and %d is %d</p><p>",firstno,secondno,gcd); printf("</p><p>The LCM of %d and %d is %d</p><p>",firstno,secondno,(firstno*secondno)/gcd); } else printf("One of the entered no. is zero:Quitting</p><p>"); } /*Function for Euclid's Procedure*/ int gcd_rec(int x, int y){ if (y == 0) return x; return gcd_rec(y, x % y); }
當上述程序執行時,會產生以下結果-
Enter the two no.s to find GCD and LCM:4 8 The GCD of 4 and 8 is 4 The LCM of 4 and 8 is 8
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