Euler Problem 5 in Clojure

Factors

(defn prime? [n]
  (cond (= n 2) true
	(= n 3) true
	:else
	(not-any? #(zero? (mod n %))(range (int (Math/sqrt n)) n))))

(def my-primes (filter prime? (iterate inc 2)))

(defn update-or-insert [m k f d]
  (if (contains? m k)
    (update-in m [k] f)
    (assoc m k d)))

(defn factors 
  ([n] (factors n (sorted-map)))
  ([n fs]   
     (cond (= n 0) fs
	   (= n 1) fs
	   (prime? n) (update-or-insert fs n inc 1)
	   :else
	   (let [f (first
		    (for [p my-primes
			  :when (zero? (mod n p))]
		      p))		      
		 ndiv (quot n f)]
	     (recur ndiv (update-or-insert fs f inc 1))))))

(defn my-power
  ([x n] (my-power x n 1))
  ([x n r]
     (if (= n 0) r
	 (recur x (dec n) (* r x)))))

; find the common set of factors for a range of numbers

(defn div-by-all [n]
  (reduce * (map #(my-power (first %) (second %))
		 (apply merge-with max (map factors (range 2 (inc n)))))))

(div-by-all 20)
232792560

(div-by-all 200)
337293588832926264639465766794841407432394382785157234228847021917234018060677390066992000