euler005.clj

; Problem 5
; 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?

(defn divisible-by? [x y]
  (zero? (mod y x)))

(defn find-sol* [n startfrom]
  (let [factors (vec (reverse (range (int (/ (inc n) 2)) (+ 1 n))))
	mingcd (* n (int (/ startfrom n)))
	start (bigint (if (zero? mingcd) n mingcd))]
    (loop [sofar start]
      (cond (every? #(divisible-by? % sofar) factors)
	    sofar
	    :else
	    (recur (+ n sofar))))))

(defn find-sol [n]
  (reduce #(find-sol* %2 %1) 2 (range 2 (inc n))))