From 8e9427d1172bf06f29e26f36c46f3e4c0c0b53c4 Mon Sep 17 00:00:00 2001
From: newt <hi@newty.dev>
Date: Wed, 9 Oct 2024 18:10:09 +0100
Subject: [PATCH] feat(problem): 5 - smallest multiple

---
 src/bin/5.rs | 52 ++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 52 insertions(+)
 create mode 100644 src/bin/5.rs

diff --git a/src/bin/5.rs b/src/bin/5.rs
new file mode 100644
index 0000000..19d8f3e
--- /dev/null
+++ b/src/bin/5.rs
@@ -0,0 +1,52 @@
+/*
+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) -> usize { 
+	if start > end {
+		panic!("You can not start on a value higher than your end value!");
+	}
+
+	let mut result: usize = 1;
+
+	for i in start..(end + 1) {
+		result = (result * i) / gcd(result, i);
+	}
+
+	return result;
+}
+
+fn main() {
+	let number = first_value_divisible_by(1, 20);
+
+	println!("The smallest number that is divisible by all integers between 1 and 20 is {number}");
+}