Accept a positive integer n as input and find the print the smallest integer that is divisible by all the integers in the range [1, n]

Question

How do I solve this question? I've intuitively understood that I am required to find the LCM of the number between [1,n] but I cannot figure out how to code this without using the math library and function defining processes in Python. I did find some solutions for C++ but they are beyond my understanding.

Answer 1

You need to multiply the numbers that are not a divisor of the other numbers

A simple (non optimal) algorithm is to descend the list of numbers and check if any smaller number is a divisor, if it is then add it to a blacklist.

Then multiply all numbers that are not blacklisted:

N = 10

number = 1
skip = set()
for i in range(N, 0, -1):
    for j in range(i-1, 1, -1):
        if j in skip:
            continue
        if not i%j:
            print(f'{j} divides {i}, skipping {j}')
            skip.add(j)
    if i not in skip:
        number *= i

output for N=10:

5 divides 10, skipping 5
2 divides 10, skipping 2
3 divides 9, skipping 3
4 divides 8, skipping 4
30240

Answer 2

Well the easiest approach without any optimization would be sth like:

def int_div(n):
    outp = 0
    while(True):
        outp += 1 
        res_list = []
        for i in range(1,n+1): res_list.append(outp%i)
        if sum(res_list) == 0:
            break
    return outp

But it works well just for small numbers <=16.