Problem#
Little Onion likes to eat candy, and he bought a lot of it. However, Little Onion bought too much candy, and he can't remember the exact number; he only remembers that the total amount of candy he has is the least common multiple of the $N$ numbers $a_1,a_2,\cdots,a_N$ recorded in his notebook. Please help Little Onion calculate how much candy he bought.
For $100%$ of the data, $1\leq N\leq 10^3,1\leq a_i\leq 10^9$.
Solution#
To summarize the problem—find the least common multiple of $n$ numbers.
Directly factor the numbers into primes, then determine the maximum power of each prime factor and multiply them together.
(This is the first time I encountered an A problem in an exam, but it's just a sign-in question QAQ)
Code#
#include<bits/stdc++.h>
#define int long long
using namespace std;
map <long long, long long>s;
const int N = 1e3 + 10;
int a[N], n;
const int mod = 1e9 + 7;
int read()
{
int f = 1, x = 0;
char ch = getchar();
while(ch < '0' || ch > '9')
{
if(ch == '-') f = -1;
ch = getchar();
}
while(ch >= '0' && ch <= '9')
{
x = 10 * x + ch - '0';
ch = getchar();
}
return f * x;
}
int fast_power(int a, int p)
{
int ans = 1;
while(p)
{
if(p & 1) ans = ans * a % mod;
a = a * a % mod;
p >>= 1;
}
return ans % mod;
}
signed main()
{
freopen("buy.in", "r", stdin);
freopen("buy.out", "w", stdout);
int ans = 1;
n = read();
for(int i = 1;i <= n;i++)
a[i] = read();
int temp;
for(int i = 1;i <= n;i++)
{
temp = a[i];
for(int j = 2;j <= temp / j;j++)
{
int c = 0;
while(temp % j == 0)
{
// cout << "qwq" << a[i] << " " << j << endl;
c++;
temp /= j;
if(c > s[j])
{
ans = (ans * j) % mod;
s[j]++;
}
}
// if(c > s[j])
// {
//// cout << "ans *=" << c - s[j] << "*"<< j <<endl;
// ans = (ans * (c - s[j]) * j) % mod;
// s[j] = c;
// }
}
if(temp > 1)
{
// cout << "qwq" << a[i] << " " << temp << endl;
if(s[temp] == 0)
{
s[temp] = 1;
// cout << "ans *= " << temp <<endl;
ans = ans * temp % mod;
}
}
}
printf("%lld", ans % mod);
return 0;
}