Conception does not have anything to do with LMP, only with ovulation.
With an ultrasound they look at the baby's growth and the development of the internal organs. At 6 weeks (plus or minus 2 days), they will see the heart for the first time. These developments take place according to a very strict schedule in early pregnancy (frst trimester and up to week 1

. For this reason early scans are very accurate (week 6 to plus or minus 2 days, week 18 to plus or minus 7 or 8 days).
The baby's age given to you is a gestational age (GA). It is 2 weeks longer than the fetal age (FA). So if you had perfect 28 day cycles with ovulation on day 14, counting backwards the GA will match your LMP date exactly and FA will match your ovulation exactly.
Since our cycles are very seldomly perfect, GA just counts back to some arbitrary day close to your LMP. GA - 14 days (the fetal age) will however always count back to around ovulation and conception.