Answer Posted / raghavendra sai

Let the three numbers in GP: a/r, a, ar---------(A)
Where '^' is power of . . .

Sum of these numbers are:
a/r +a +ar = 38
a(1\r+1+r) = 38 ---- (1)
Product of these numbers are:
a^3 = 1728
= (12)^3
a = 12

Putting the value of a in (1) you will get:

12(1\r+1+r) = 38

And factorising, we get
r = 2/3 or r = 3/2

Sub. the r and a value in (A), we get

8,12,18 or 18,12,8. When a = 12

And smallest no. is 8.

Read more: http://wiki.answers.com/Q/Find_the_smallest_number_in_a_GP_whose_sum_is_38_and_product_1728#ixzz1hFVTQBE3

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