freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-350-constraining-the-least-greatest-and-the-greatest-least.english.md

id	challengeType	title	forumTopicId
5900f4cb1000cf542c50ffdd	5	Problem 350: Constraining the least greatest and the greatest least	302010

Description

A list of size n is a sequence of n natural numbers. Examples are (2,4,6), (2,6,4), (10,6,15,6), and (11).

The greatest common divisor, or gcd, of a list is the largest natural number that divides all entries of the list. Examples: gcd(2,6,4) = 2, gcd(10,6,15,6) = 1 and gcd(11) = 11.

The least common multiple, or lcm, of a list is the smallest natural number divisible by each entry of the list. Examples: lcm(2,6,4) = 12, lcm(10,6,15,6) = 30 and lcm(11) = 11.

Let f(G, L, N) be the number of lists of size N with gcd ≥ G and lcm ≤ L. For example:

f(10, 100, 1) = 91. f(10, 100, 2) = 327. f(10, 100, 3) = 1135. f(10, 100, 1000) mod 1014 = 3286053.

Find f(106, 1012, 1018) mod 1014.

Instructions

Tests

tests:
  - text: <code>euler350()</code> should return 84664213.
    testString: assert.strictEqual(euler350(), 84664213);

Challenge Seed

function euler350() {
  // Good luck!
  return true;
}

euler350();

Solution

// solution required