2.4 KiB
2.4 KiB
id | title | challengeType | forumTopicId |
---|---|---|---|
5a23c84252665b21eecc7edf | Least common multiple | 5 | 302301 |
Description
The least common multiple of 12 and 18 is 36, because 12 is a factor (12 × 3 = 36), and 18 is a factor (18 × 2 = 36), and there is no positive integer less than 36 that has both factors. As a special case, if either m or n is zero, then the least common multiple is zero.
One way to calculate the least common multiple is to iterate all the multiples of m, until you find one that is also a multiple of n.
If you already have gcd for greatest common divisor, then this formula calculates lcm.
\operatorname{lcm}(m, n) = \frac{|m \times n|}{\operatorname{gcd}(m, n)}
Instructions
Compute the least common multiple of an array of integers. Given m and n, the least common multiple is the smallest positive integer that has both m and n as factors.
Tests
tests:
- text: <code>LCM</code> should be a function.
testString: assert(typeof LCM == 'function');
- text: <code>LCM([2, 4, 8])</code> should return a number.
testString: assert(typeof LCM([2, 4, 8]) == 'number');
- text: <code>LCM([2, 4, 8])</code> should return <code>8</code>.
testString: assert.equal(LCM([2, 4, 8]), 8);
- text: <code>LCM([4, 8, 12])</code> should return <code>24</code>.
testString: assert.equal(LCM([4, 8, 12]), 24);
- text: <code>LCM([3, 4, 5, 12, 40])</code> should return <code>120</code>.
testString: assert.equal(LCM([3, 4, 5, 12, 40]), 120);
- text: <code>LCM([11, 33, 90])</code> should return <code>990</code>.
testString: assert.equal(LCM([11, 33, 90]), 990);
- text: <code>LCM([-50, 25, -45, -18, 90, 447])</code> should return <code>67050</code>.
testString: assert.equal(LCM([-50, 25, -45, -18, 90, 447]), 67050);
Challenge Seed
function LCM(A) {
}
Solution
function LCM(A) {
var n = A.length,
a = Math.abs(A[0]);
for (var i = 1; i < n; i++) {
var b = Math.abs(A[i]),
c = a;
while (a && b) {
a > b ? (a %= b) : (b %= a);
}
a = Math.abs(c * A[i]) / (a + b);
}
return a;
}