\(\dfrac{45}{46}\times\dfrac{49}{50}\times\dfrac{180}{103}\times\dfrac{92}{45}\times\dfrac{50}{49}\times\dfrac{103}{90}\)
\(=\left(\dfrac{45}{46}\times\dfrac{92}{45}\right)\times\left(\dfrac{49}{50}\times\dfrac{50}{49}\right)\times\left(\dfrac{180}{103}\times\dfrac{103}{90}\right)\)
\(=\left(\dfrac{45\times46\times2}{46\times45}\right)\times\left(\dfrac{49\times50}{50\times49}\right)\times\left(\dfrac{90\times2\times103}{103\times90}\right)\)
\(=2\times1\times2\)
\(=4\)