# 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 = 2^{a} x 3^{b}

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.