From 57d48ed16ea6a4b419ee242a4800c8e62adf1fa7 Mon Sep 17 00:00:00 2001
From: Simon Waldherr <git@simon.waldherr.eu>
Date: Tue, 29 Oct 2024 19:20:40 +0100
Subject: [PATCH] add common divisor and common multiple

---
 mathematics/greatest_common_divisor.r | 24 ++++++++++++++++++++++++
 mathematics/least_common_multiple.r   | 27 +++++++++++++++++++++++++++
 2 files changed, 51 insertions(+)
 create mode 100644 mathematics/greatest_common_divisor.r
 create mode 100644 mathematics/least_common_multiple.r

diff --git a/mathematics/greatest_common_divisor.r b/mathematics/greatest_common_divisor.r
new file mode 100644
index 00000000..9c2b94c1
--- /dev/null
+++ b/mathematics/greatest_common_divisor.r
@@ -0,0 +1,24 @@
+# GCD Calculation using Euclidean Algorithm
+find_gcd <- function(a, b) {
+  
+  #' @description Computes the Greatest Common Divisor (GCD) of two integers.
+  #' @param a Integer
+  #' @param b Integer
+  #' @usage find_gcd(a, b)
+  #' @details This function uses the Euclidean algorithm to find the GCD.
+  #' GCD is essential in various mathematical contexts, particularly in
+  #' simplification of fractions and number theory applications.
+  #' @references https://en.wikipedia.org/wiki/Euclidean_algorithm
+  
+  while (b != 0) {
+    temp <- b
+    b <- a %% b
+    a <- temp
+  }
+  
+  return(abs(a))
+}
+
+# Examples
+print(find_gcd(48, 18))  # expected 6
+print(find_gcd(54, 24))  # expected 6
diff --git a/mathematics/least_common_multiple.r b/mathematics/least_common_multiple.r
new file mode 100644
index 00000000..d440f29c
--- /dev/null
+++ b/mathematics/least_common_multiple.r
@@ -0,0 +1,27 @@
+# LCM Calculation
+find_lcm <- function(a, b) {
+  
+  #' @description Computes the Least Common Multiple (LCM) of two integers.
+  #' @param a Integer
+  #' @param b Integer
+  #' @usage find_lcm(a, b)
+  #' @details This function uses the relationship between GCD and LCM,
+  #' i.e., LCM(a, b) = |a * b| / GCD(a, b).
+  #' LCM is useful in fraction operations and periodicity calculations.
+  #' @references https://en.wikipedia.org/wiki/Least_common_multiple
+  
+  gcd <- function(x, y) {
+    while (y != 0) {
+      temp <- y
+      y <- x %% y
+      x <- temp
+    }
+    return(abs(x))
+  }
+  
+  return(abs(a * b) / gcd(a, b))
+}
+
+# Examples
+print(find_lcm(48, 18))  # expected 144
+print(find_lcm(54, 24))  # expected 216