49 lines
1.2 KiB
Markdown
49 lines
1.2 KiB
Markdown
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---
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id: 5900f4cb1000cf542c50ffdd
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title: 'Problem 350: Constraining the least greatest and the greatest least'
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challengeType: 5
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forumTopicId: 302010
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dashedName: problem-350-constraining-the-least-greatest-and-the-greatest-least
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---
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# --description--
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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).
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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.
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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.
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Let f(G, L, N) be the number of lists of size N with gcd ≥ G and lcm ≤ L. For example:
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f(10, 100, 1) = 91. f(10, 100, 2) = 327. f(10, 100, 3) = 1135. f(10, 100, 1000) mod 1014 = 3286053.
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Find f(106, 1012, 1018) mod 1014.
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# --hints--
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`euler350()` should return 84664213.
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```js
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assert.strictEqual(euler350(), 84664213);
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```
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# --seed--
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## --seed-contents--
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```js
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function euler350() {
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return true;
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}
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euler350();
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```
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# --solutions--
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```js
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// solution required
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```
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