perplexus.info :: Just Math : lcm and power poser

lcm and power poser (Posted on 2015-12-02)

Determine the total number of values of a positive integer N such that:
lcm (6⁶, 8⁸, N)= 12¹²

See The Solution Submitted by K Sengupta

Rating: 3.0000 (2 votes)

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D2	Comment 1 of 1

12^12 = 3^12 * 2^24

6^6 = 2^6 * 3^6

8^8 = 2^24

-------------------------

So, the only N that work are

3^12 * (2^0 or 2^1 or ... 2^24)

Altogether, 25 different values

The answer is the same without 6^6.

Posted by Steve Herman on 2015-12-02 21:10:12

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