Statement

2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.

What is the smallest number that is evenly divisible by all of the numbers from 1 to 20?

Solution

The technique I used to solve this problem is quite simple. You need to find the LCM(Least Common Multiple)
of the first 20 numbers.

To do this I set up a list with them, and then starting from the second(2) I pass through the list(from the next
that I have taken) dividing the others in case it's possible. This way i take all the prime factors that are already
taken into account.

if __name__ == '__main__':
    n = 20
    lt = list(range(1, n+1))
    for i in range(1, n):
        x = lt[i]
        index = i + 1
        while index < n:
            if (lt[index] % x) == 0:
                lt[index] //= x
            index += 1
    result = 1
    for elem in lt:
        result *= elem
    print("The result is:", result)

The Python code is available for download here.