5.rs

/*
Problem 5 - Smallest multiple

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 positive number that is  evenly divisible  by all of the numbers from 1 to 20?
*/

// Euclidean algorithm for finding GCD
fn gcd(a: usize, b: usize) -> usize {
    let mut x = a;
    let mut y = b;
    let mut r: usize = 1; // temporary initial value

    while r != 0 {
        if x < y {
            let temp = x;
            x = y;
            y = temp;
        }

        r = x % y;

        if r == 0 {
            break;
        } else {
            x = y;
            y = r;
        }
    }

    return y;
}

fn first_value_divisible_by(start: usize, end: usize) -> Option<usize> {
    if start > end {
        return None;
    }

    let mut result: usize = 1;

    for i in start..(end + 1) {
        result = (result * i) / gcd(result, i);
    }

    return Some(result);
}

pub fn main() {
    let number = first_value_divisible_by(1, 20).unwrap();

    println!("The smallest number that is divisible by all integers between 1 and 20 is {number}");
}