import java.io.; import java.util.; import java.text.; import java.math.; import java.util.regex.*;

public class Solution {

public static void main(String[] args) {
    Scanner in = new Scanner(System.in);
    int t = in.nextInt();
    for(int i = 0; i < t; i++){
        int n = in.nextInt();
        int ans = smallestDivisibleNumber(n);
        System.out.println(ans);

    }
}
 private static int smallestDivisibleNumber(int n) {
    int ans = 1;
    for (int i = 2; i <= n; i++) {
        ans = lcm(ans, i);
    }
    return ans;
}

private static int lcm(int a, int b) {
    return (a * b) / gcd(a, b);
}

private static int gcd(int a, int b) {
    if (b == 0) {
        return a;
    }
    return gcd(b, a % b);
}

}

Python Solution, I cut some factor processing through prime checking

import math


def isPrime(n):
    if n == 1:
        return False
    if n % 2 == 0:
        return False
    for i in range(3, int(math.sqrt(n))+1, 2):
        if n % i == 0:
            return False
    return True


for t in range(int(input())):
    n = int(input())
    s = n
    while True:
        if not isPrime(s):
            for i in range(2, n + 1):
                if s % i != 0:
                    break
            else:
                print(s)
                break
        if s % 2 == 1:
            s += 1
        else:
            s += 2

python 3

t = int(input().strip())
for a0 in range(t):
    n = int(input().strip())
    num = 0
    while True:
        num += 1
        isOutput = True
        for i in range(1, n + 1):
            if num % i != 0:
                isOutput = False
                break
        if isOutput:
            break
    print(num)

100 points in just a millisecond:

1) find prime numbers from 1 to N. 2) find maximum power of prime number. 3) multiply each prime powers.

Hint: You dont need to calculate nonprime numbers because you always have enough primes to make them up

int result = 1;
for (int i = 1; i <= n; i++) {
  if (isPrime(i)) {
    int r1 = 1;
    while (r1 * i <= n)
      r1 *= i;
    result *= r1;
  }
}
return result;

import java.math.BigInteger;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int t = sc.nextInt();
    for (int i = 0; i < t; i++) {
        int n = sc.nextInt();
        System.out.println(lcm(n));
    }
    sc.close();
}

private static BigInteger lcm(int n) {
    BigInteger lcm = BigInteger.valueOf(1);
    for (int i = 2; i <= n; i++) {
        lcm = lcm(lcm, i);
    }
    return lcm;
}

private static BigInteger lcm(BigInteger a, int b) {
    return a.multiply(BigInteger.valueOf(b))
             .divide(a.gcd(BigInteger.valueOf(b)));
}
}