The last traded price or LTP is the price at which the stock was most recently sold. The LTP may or may not be the same as the closing price of the day, as the closing price in some exchanges is calculated as the weighted average of the last few minutes of the trade. It must be noted that the last traded price is simply the price at which the previous trade of the security was executed at any given point in time.
One must remember that LTP is always a historical number, and the recorded LTP could only be of a few seconds ago. Furthermore, when you buy a share, it may be the case that you may have bought it at its LTP. Since trades take place every second, it may not be possible that you have traded shares at their LTP.