Question

Find the smallest possible integer value for n for which 99n is a multiple of 24​

Answer 1

Answer:

8 is the smallest possible integer value for n .

Answer 2

Concept:

To answer this question we recall the definition of L.C.M as we will require this concept to solve.

L.C.M is the least common multiple of two or three or more numbers. Example: the L.C.M of 4 and 6 is 12

Given:

We are given 99n(where n is an unknown variable) and 24

To find:

We are asked to find the smallest integer value for n for which 99n is a multiple of 24.

Solution:

We first take the L.C.M  of 99 and 24.

The list of common multiples are= 3,33 and 8.

Multiplying the multiples we get the L.C.M to be 3x33x8=792.

Now, we are asked to find the integer of n in 99n which is (99xn).

So, we need to divide 792 by 99 to find the value of n

99)792(8

   -792

__________

       0

Hence, the integer value of n is 8