If the least common multiple of two numbers 1728 and K is 5184 then how many values of K are possibl...........

Quantitative Aptitude (CGL) Number System

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If the least common multiple of two numbers, 1728 and K is 5184, then how many values of K are possible?

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Explanation:

One of the numbers is 1728 (1728 = 3^3* 2^6) and LCM is 5184. Now, 5184 is 3 times 1728. Therefore the Other Number has to be having one of the factors as 3^4, which is 81.
So, now the 7 possibilities for the other number are:
81, 81*2, 81*4, 81*8, 81*16, 81*32 and 81*64 i. e.
81, 162, 324, 648, 1296, 2592 and 5184.
Thus 7 values of k are possible.