Question

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

Answer 1

1728 values of k are possible

Answer 2

Step-by-step 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.