2.9 KiB
id | title | challengeType |
---|---|---|
5a23c84252665b21eecc7edf | Least common multiple | 5 |
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 intergers. 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', '<code>LCM</code> should be a function.');
- text: <code>LCM([2, 4, 8])</code> should return a number.
testString: assert(typeof LCM([2, 4, 8]) == 'number', '<code>LCM([2, 4, 8])</code> should return a number.');
- text: <code>LCM([2, 4, 8])</code> should return <code>8</code>.
testString: assert.equal(LCM([2, 4, 8]), 8, '<code>LCM([2, 4, 8])</code> should return <code>8</code>.');
- text: <code>LCM([4, 8, 12])</code> should return <code>24</code>.
testString: assert.equal(LCM([4, 8, 12]), 24, '<code>LCM([4, 8, 12])</code> should return <code>24</code>.');
- text: <code>LCM([3, 4, 5, 12, 40])</code> should return <code>120</code>.
testString: assert.equal(LCM([3, 4, 5, 12, 40]), 120, '<code>LCM([3, 4, 5, 12, 40])</code> should return <code>120</code>.');
- text: <code>LCM([11, 33, 90])</code> should return <code>990</code>.
testString: assert.equal(LCM([11, 33, 90]), 990, '<code>LCM([11, 33, 90])</code> should return <code>990</code>.');
- 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, '<code>LCM([-50, 25, -45, -18, 90, 447])</code> should return <code>67050</code>.');
Challenge Seed
function LCM(A) {
// Good luck!
}
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;
}