ugly numbers

I lifted it from the career cup site
Design an algorithm to find the kth number divisible by only 3 or 5 or 7. That is, the only factors of these numbers should be 3,5 and 7.

What I have in mind -

Generating the numbers which have prime factors as only 3,5, 7 is not a big thing. but doing so in a sorted order is a little tricky.
Let's call the exponents of 3,5,7 as a,b and c repectively.
Claim: The order of numbers with a = b = c = n to a = b = c = n+1 would be unchanged for any n >= 0.
And that gives an idea to program it. We have to find an order between to successive exponents. Lets start with n = 0. Then we have to find all the numbers ordered ( with their exponents known ) less than 105 ( 3*5*7 ) and greater than 1.
Way 1 -
Write a program to generate all the numbers which are factors of 3 or 5 or 7 ( with their factors recorded. And then keep increasing these factors...
For exp if the factors have exponents (a1,b1,c1), (a2,b2,c2)....(am,bm,cm). then the next cycle of increasing numbers will have exp ( a1+1, b1+1, c1+1 )....(am+1, bm+1, cm+1).
Way 2 -
Generale the numbers thru' the exp. Its clear that they are upper bounded, for n = 0, as a < 5, b < 3, c < 3. So 3 for loops and get all numbers which fall below 105, get their corresponding exp and thats it.