If the least common multiple of two numbers, 1728 and K is 5184,

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

A. 11

B. 8

C. 6

D. 7

Please scroll down to see the correct answer and solution guide.

Right Answer is: D

SOLUTION

The uncommon factor of K and 1728 = 5184/1728 = 3
Let K = 2a x 3b


Now, because we take maximum powers of the prime factors in the L.C.M
Hence K is a multiple of  and power to 2 is less than 6.
K =
Total possible values of m are
Hence number of possible values of K are 7.