Least Common Multiple
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Least Common Multiple
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 34436 Accepted Submission(s): 12968
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
23 5 7 156 4 10296 936 1287 792 1
Sample Output
10510296
Source
East Central North America 2003, Practice
思路:这个题好像以前做过,但是忘了思路了,百度了一下,现在知道了。求所有数的最小公倍数,就是先两个求最小公倍数,然后所得的公倍数再与下一个数求最小公倍数。。两个数乘积除以最大公约数等于最小公倍数。
知道方法了,那么写代码就比较容易了。。我注释掉的代码是我的方法,求最大公约数,但是提交说超时了。。百度一下,可以用欧几里得定理。这样就ac了。。
节省时间,记住这个方法求最大公约数。
int gys(int a,int b) //欧几里得求最大公约数
{
if(b==0)
return a;
return gys(b,a%b);
}
#include<iostream>using namespace std;int gys(int a,int b){ /* int i,result; //此方法超时 for(i=1;i<=a;i++) { if(a%i==0 && b%i==0) result=i; } result=a*b/result; return result;*/ if(b==0) return a; //欧几里得求最大公约数 return gys(b,a%b);}int main(){ int T,n,i,a[1000]; cin>>T; while(T--) { cin>>n; for(i=0;i<n;i++) cin>>a[i]; for(i=0;i<n-1;i++) //x x x x x { a[i+1]=a[i]/gys(a[i],a[i+1])*a[i+1]; } cout<<a[i]<<endl; } return 0;}
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