The greatest common factor of 400 and 576 is 16, so the least common multiple is ...
... 400 × 576 / 16 = 400 × 36
The smallest positive integer x is 36.
_____
<em>Comment on greatest common factor</em>
There are at least a couple of ways to find the greatest common factor (GCG) of 400 and 576. One is to simply factor the numbers.
... 400 = 2⁴×5²
... 576 = 2⁶×3²
The largest factor common to both these numbers is 2⁴ = 16.
___
Another way is to use Euclid's algorithm.
... 576/400 = 1 r 176
... 400/176 = 2 r 48
... 176/48 = 3 r 32
... 48/32 = 1 r 16
... 32/16 = 2 r 0 . . . . . so 16 is the GCF
_____
<em>Comment on least common multiple</em>
The least common multiple is the product of unique prime factors to the highest power that they appear in either number. Here, that is ...
... 2⁶×3²×5² = LCM(400, 576)
... = (2²×3²)×400 = 36×400
This can also be found by
... LCM(a, b) = a×b/GCF(a, b) . . . . . which is what we did above
