ocaml: phase 5.1 euler5.ml baseline (smallest multiple of 1..20 = 232792560)

Iteratively takes lcm of running result with i:

  let rec gcd a b = if b = 0 then a else gcd b (a mod b)
  let lcm a b = a * b / gcd a b
  let euler5 n =
    let r = ref 1 in
    for i = 2 to n do
      r := lcm !r i
    done;
    !r

  euler5 20 = 232792560
            = 2^4 * 3^2 * 5 * 7 * 11 * 13 * 17 * 19

Tests gcd_lcm composition (iter 140) on a fresh problem.

109 baseline programs total.

lib/ocaml/baseline/euler5.ml

@@ -0,0 +1,11 @@
+let rec gcd a b = if b = 0 then a else gcd b (a mod b)
+let lcm a b = a * b / gcd a b
+let euler5 n =
+  let r = ref 1 in
+  for i = 2 to n do
+    r := lcm !r i
+  done;
+  !r
+;;
+
+euler5 20

lib/ocaml/baseline/expected.json

@@ -27,6 +27,7 @@
   "exception_user.ml": 26,
   "euler1.ml": 233168,
   "euler2.ml": 4613732,
+  "euler5.ml": 232792560,
   "euler6.ml": 25164150,
   "euler9.ml": 31875000,
   "expr_eval.ml": 16,

plans/ocaml-on-sx.md

@@ -407,6 +407,12 @@ _Newest first._
   binary search tree (`type 'a tree = Leaf | Node of 'a * 'a tree *
   'a tree`) with insert + in-order traversal. Tests parametric ADT,
   recursive match, List.append, List.fold_left.
+- 2026-05-09 Phase 5.1 — euler5.ml baseline (Project Euler #5,
+  smallest number divisible by all 1..20 = 232792560). Iteratively
+  takes lcm of running result with i for i=2..n; lcm via gcd via
+  Euclidean. 232792560 = 2^4 * 3^2 * 5 * 7 * 11 * 13 * 17 * 19.
+  Tests two-line gcd/lcm + for-loop accumulator pattern. 109
+  baseline programs total.
 - 2026-05-09 Phase 5.1 — partition.ml baseline (stable partition by
   predicate, 30*100 + 25 = 3025). Two ref lists accumulating in
   reverse, then List.rev'd — preserves original order. Test: