freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-350-constraining-the-least-greatest-and-the-greatest-least.md

id, title, challengeType, forumTopicId, dashedName

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

--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:

$$\begin{align} & f(10, 100, 1) = 91 \\ & f(10, 100, 2) = 327 \\ & f(10, 100, 3) = 1135 \\ & f(10, 100, 1000)\bmod {101}^4 = 3\,286\,053 \end{align}$$

Find f({10}^6, {10}^{12}, {10}^{18})\bmod {101}^4.

--hints--

leastGreatestAndGreatestLeast() should return 84664213.

assert.strictEqual(leastGreatestAndGreatestLeast(), 84664213);

--seed--

--seed-contents--

function leastGreatestAndGreatestLeast() {

  return true;
}

leastGreatestAndGreatestLeast();

--solutions--

// solution required