Problems

# The Least Common Multiple

# The Least Common Multiple

Find the Least Common Multiple for all integers from **1** to **n**.

The Least Common Multiple of positive integers `a`

, _{1}`a`

, _{2}`...`

, `a`

is an integer _{k}**A**, such that **A** is divisible by `a`

for all _{i}**i** from **1** to **k**, and **A** is the least positive integer with such property.

#### Input

One integer **n** (**1** ≤ **n** ≤ **1000**).

#### Output

Print one number - the Least Common Multiple of all numbers from **1** to **n**.

Input example #1

3

Output example #1

6