SOLUTION: the least integer power of 12 that is divisible by 18 raised to the power 180,,is 12 raised to power 120 12 raised to power 180 12 raised to power 240 12 raised to powe

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Question 1062576: the least integer power of 12 that is divisible by 18 raised to the power 180,,is
12 raised to power 120
12 raised to power 180
12 raised to power 240
12 raised to power 360
i saw this question solved on your website and the answer was zero , but thats incorrect as thats not even an option. can someone please help explain the answer. for convenience the answer is 12 raised to power 360 ,,, but how///
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

18180 = (2132)180 = 21803360

Let N be the least integer power of 12 that is divisible by 18180.

12N = (2231)N = 22N3N

So we divide:

%282%5E%282N%29%2A3%5EN%29%2F%282%5E180%2A3%5E360%29 = 2(2N-180)3(N-360).

The smallest integers N can be must be just enough to make
sure those powers of 2 and 3 are not negative.

So N-360 = 0 or N = 360, 

(and certainly then 2N-180 = 360-180=180 is not negative.)

So N = 360.

Edwin