Vaibhav wrote a certain number of positive prime numbers on a piece of paper. Vikram wrote down the product of all the possible triplets among those numbers. For every pair of numbers written by Vikram, Vishal wrote down the corresponding $\text{GCD}.$ If $90$ of the numbers written by Vishal were prime, how many numbers did Vaibhav write?
- $6$
- $8$
- $10$
- Cannot be determined