(*
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 number that is evenly divisible by all of the numbers from 1 to 20?
*)

let lcm l =
  (* remove multiples of x in l *)
  let rem_mult x l = List.map ( fun y -> if (y mod x=0) then (y/x) else y) l in
  (* iterative reduce multiples of list members *)
  let rec red_mult l =
    match l with
    [] -> []
    | h::t -> h::(red_mult (rem_mult h t))
  in
  List.fold_left ( * ) 1 ( red_mult l )
;;

(* proper divisors below n: list of numbers below n, but greater than 1 *)
let pdb n =
  let rec pdb n l =
    if (n<2) 
    then l
    else pdb (n-1) (n::l)
  in
    pdb n []
;;

Printf.printf "%d\n" (lcm (pdb 20));