diff --git a/input/08-test-1 b/input/08-test-1
new file mode 100644
index 0000000..34ffa8a
--- /dev/null
+++ b/input/08-test-1
@@ -0,0 +1,5 @@
+LLR
+
+AAA = (BBB, BBB)
+BBB = (AAA, ZZZ)
+ZZZ = (ZZZ, ZZZ)
\ No newline at end of file
diff --git a/input/08-test-2 b/input/08-test-2
new file mode 100644
index 0000000..a8e2c98
--- /dev/null
+++ b/input/08-test-2
@@ -0,0 +1,10 @@
+LR
+
+11A = (11B, XXX)
+11B = (XXX, 11Z)
+11Z = (11B, XXX)
+22A = (22B, XXX)
+22B = (22C, 22C)
+22C = (22Z, 22Z)
+22Z = (22B, 22B)
+XXX = (XXX, XXX)
\ No newline at end of file
diff --git a/src/bin/08.rs b/src/bin/08.rs
new file mode 100644
index 0000000..86c5e77
--- /dev/null
+++ b/src/bin/08.rs
@@ -0,0 +1,144 @@
+use aoc2023::lcm;
+use std::collections::HashMap;
+
+const INPUT: &str = include_str!("../../input/08");
+const TEST_INPUT_1: &str = include_str!("../../input/08-test-1");
+const TEST_INPUT_2: &str = include_str!("../../input/08-test-2");
+
+fn main() {
+    assert_eq!(part1(TEST_INPUT_1), 6, "Part 1");
+    println!("Part 1: {}", part1(INPUT));
+    assert_eq!(part2(TEST_INPUT_2), 6, "Part 2");
+    println!("Part 2: {}", part2(INPUT));
+}
+
+fn part1(input: &str) -> usize {
+    let start = "AAA".to_string();
+    let end = |location: &str| location == "ZZZ";
+    Map::parse(input).count_steps(start, end)
+}
+
+fn part2(input: &str) -> usize {
+    let map = Map::parse(input);
+    let end = |location: &str| location.ends_with('Z');
+
+    map.starting_locations()
+        .map(|start| map.count_steps(start, end))
+        .reduce(lcm)
+        .unwrap()
+}
+
+struct Map {
+    transitions: HashMap<String, Directions>,
+    instructions: Vec<Instruction>,
+}
+
+impl Map {
+    /// Apply a list of instructions.
+    fn follow(&self, from: String) -> String {
+        self.instructions
+            .iter()
+            .fold(from, |location, &instruction| {
+                self.step(location, instruction)
+            })
+    }
+
+    /// Apply a single instruction.
+    fn step(&self, from: String, instruction: Instruction) -> String {
+        let direction = self.transitions.get(&from).unwrap();
+        match instruction {
+            Instruction::Left => direction.left.clone(),
+            Instruction::Right => direction.right.clone(),
+        }
+    }
+
+    fn starting_locations(&self) -> impl Iterator<Item = String> + '_ {
+        self.transitions
+            .keys()
+            .filter(|k| k.ends_with('A'))
+            .map(|k| k.to_string())
+    }
+
+    fn count_steps(&self, start: String, end: impl Fn(&str) -> bool) -> usize {
+        let mut location = start;
+        let mut steps = 0;
+
+        while !end(&location) {
+            location = self.follow(location);
+            steps += self.instructions.len();
+        }
+
+        steps
+    }
+
+    fn parse(input: &str) -> Self {
+        let mut lines = input.lines();
+        let instructions = lines
+            .next()
+            .unwrap()
+            .chars()
+            .map(Instruction::parse)
+            .collect();
+        let transitions = lines
+            .skip(1)
+            .map(Transition::parse)
+            .map(|t| (t.from, t.directions))
+            .collect();
+        Self {
+            instructions,
+            transitions,
+        }
+    }
+}
+
+struct Directions {
+    left: String,
+    right: String,
+}
+
+impl Directions {
+    fn parse(tuple: &str) -> Self {
+        let (left, right) = tuple
+            .strip_prefix('(')
+            .unwrap()
+            .strip_suffix(')')
+            .unwrap()
+            .split_once(", ")
+            .unwrap();
+        Self {
+            left: left.to_string(),
+            right: right.to_string(),
+        }
+    }
+}
+
+#[derive(Copy, Clone)]
+enum Instruction {
+    Left,
+    Right,
+}
+
+impl Instruction {
+    fn parse(c: char) -> Self {
+        match c {
+            'L' => Self::Left,
+            'R' => Self::Right,
+            other => panic!("unknown instruction '{other}'"),
+        }
+    }
+}
+
+struct Transition {
+    from: String,
+    directions: Directions,
+}
+
+impl Transition {
+    fn parse(line: &str) -> Self {
+        let (from, directions) = line.split_once(" = ").unwrap();
+        Self {
+            from: from.to_string(),
+            directions: Directions::parse(directions),
+        }
+    }
+}
diff --git a/src/lib.rs b/src/lib.rs
index cac850f..6673bea 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -1,5 +1,8 @@
-use std::fmt::{Debug, Display};
-use std::str::FromStr;
+use std::{
+    fmt::{Debug, Display},
+    ops::{Div, Mul, Rem},
+    str::FromStr,
+};
 
 /// Parse a whitespace separated list of things.
 ///
@@ -27,3 +30,46 @@ where
 {
     format!("{a}{b}").parse().unwrap()
 }
+
+/// Return the greatest common divisor.
+///
+/// https://en.wikipedia.org/wiki/Euclidean_algorithm
+pub fn gcd<T>(mut a: T, mut b: T) -> T
+where
+    T: PartialEq + Default + Rem<Output = T> + Copy,
+{
+    let zero = T::default();
+    while b != zero {
+        (a, b) = (b, a % b);
+    }
+
+    a
+}
+
+/// Return the least common multiple.
+///
+/// https://en.wikipedia.org/wiki/Least_common_multiple
+pub fn lcm<T>(a: T, b: T) -> T
+where
+    T: PartialEq + Default + Rem<Output = T> + Div<Output = T> + Mul<Output = T> + Copy,
+{
+    let gcd = gcd(a, b);
+    a / gcd * b
+}
+
+#[cfg(test)]
+mod test {
+    use crate::*;
+
+    #[test]
+    fn test_gcd() {
+        assert_eq!(gcd(252, 105), 21);
+        assert_eq!(gcd(105, 252), 21);
+    }
+
+    #[test]
+    fn test_lcm() {
+        assert_eq!(lcm(4, 6), 12);
+        assert_eq!(lcm(6, 4), 12);
+    }
+}