How to understand hamming numbers on fingers?

Question

Algorithms

I can’t understand this, please describe the algorithm in js or explain?
The Hamming number is a natural number of the form 2i3j5k for some non-negative integers i, j and k.

Answer 1

Not 2i3j5k, but 2 ⁱ ×3 ^j ×5 ^k
This means that when factoring a number into prime factors, we get only 2, 3 and 5.
1 = 2 ⁰ ×3 ⁰ ×5 ⁰
3 = 2 ⁰ ×3 ¹ ×5 ⁰
15 = 2 ⁰ ×3 ¹ ×5 ¹
30 = 2 ¹ ×3 ¹ ×5 ¹
60 = 2 ² ×3 ¹ ×5 ¹
90 = 2 ¹ ×3 ² ×5 ¹
etc.