Description for Correct answer:
Let the two consecutive odd numbers are x and x + 2.

According to the question,

\( \Large x \left(x+2\right)=19043 \)

\( \Large x^{2}+2x-19043=0 \)

\( \Large x^{2}+139x-137x-19043=0 \)

\( \Large x \left(x+139\right)-137 \left(x+139\right)=0 \)

\( \Large \left(x+139\right) \left(x-137\right)=0 \)

= x = 137, -139

x = 137 [ignore -ve sign]

So, the smallest one is 137.