add common divisor and common multiple

mathematics/greatest_common_divisor.r

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+# 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

mathematics/least_common_multiple.r

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+# 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