杭电1019

Least Common Multiple

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 37254    Accepted Submission(s): 14023

Problem Description

The least common multiple (LCM) of a set of positive integers is the smallest positive integer which is divisible by all the numbers in the set. For example, the LCM of 5, 7 and 15 is 105.

 

 

Input

Input will consist of multiple problem instances. The first line of the input will contain a single integer indicating the number of problem instances. Each instance will consist of a single line of the form m n1 n2 n3 ... nm where m is the number of integers in the set and n1 ... nm are the integers. All integers will be positive and lie within the range of a 32-bit integer.

 

 

Output

For each problem instance, output a single line containing the corresponding LCM. All results will lie in the range of a 32-bit integer.

 

 

Sample Input

2 3 5 7 15 6 4 10296 936 1287 792 1

 

 

Sample Output

105 10296

 

这题的大致意思是第一行输入有几个例子，后面几行首位是代表这一个例子有几个元素，然后求这几个元素的最小公倍数；

我用的方法是 最小公倍数=a*b-（a,b）的最大公倍数；先求出前两个数的最小公倍数，然后再拿这个公倍数跟后面几个去比较，依次下去；

最大公约数我用的是递归函数做的 具体方法是 辗转相除法；

下面是我的代码

 1 #include<stdio.h>

 2 __int64 gcd(__int64 n,__int64 m)//辗转相除法

 3 {

 4     if(m==0)

 5     return n;

 6     else

 7     return gcd(m,n%m);

 8 }

 9 int main()

10 {

11     int i,n,m;

12     __int64 a[100],min,max,t;

13     

14     scanf("%d",&n);

15     while(n--)

16     {

17         scanf("%d",&m);

18         for(i=0;i<m;i++)

19         {

20             scanf("%I64d",&a[i]);

21         }

22         

23             min=a[0];

24             for(i=1;i<m;i++)

25             {

26                 if(min<a[i])

27                 {

28                     t=min;

29                     min=a[i];

30                     a[i]=t;    

31                 }

32                 max=gcd(min,a[i]);

33                 min=min*a[i]/max;

34                 

35             }

36         printf("%I64d\n",min);    

37         

38     }

39 }