Alright, let's work through 5177 times 374 step by step
5177 × 374 = 374 × (5177)
+ 374 × 7 that equals 2618
+ 374 × 70 that results in 26180
+ 374 × 100 resulting in 37400
+ 374 × 5000 that equals 1870000

= 1936198
