I had 2 ultrasounds done one at 21 weeks of pregnancy and another at 23 and they both matched my LMP calculation. Does this mean its accurate?

Accurate for what ? Due date, conception date ? Date of your Last Monthly Period ?

They are what they are, great professional estimated guesses based on average sizes and development at certain times.
They are good with give or take a week or two.

Yes, it is accurate according to your LMP.

My due date and the day I conceived.

They are pretty accurate for due date, based on the measurements of the baby. As for conception date, that is only a general time frame based on your LMP.

But there is no real issue for conception dates unless there were multiple sex partners. As long as they were not within 2 or 3 weeks of each other it should be OK to work it out.

So please define exactly what you are trying to find out, if it is conception date and multiple partners how close together were the partners?