$8+8+5=9+9+3=10+10+1=21$, so after we removing $21$ cards, the number of the remaining cards can be divisible by $8, 9,$ and $10.$ 
Vivian has many barbie cards. If she puts $8$ cards in each group, there will be $5$ cards left. If she puts $9$ cards in each group, there will be $3$ cards left. If she puts $10$ cards in each group, there will be $1$ card left. How many cards at least should Vivian take away, so that the remaining number of cards can be divisible by $8,$ $9,$ and $10$? 

a: $$36$$ 
b: $$15$$ 
c: $$23$$ 
d: $$21$$ 
e: $$9$$ 