A small wheel of radius 1.4cm drives a large wheel of radius 15cm by having their circumferences pressed together. If the small wheel turns at 407 rad/s, how fast does the larger one turn? Answer in rad/s

This is what I was thinking...

radius of smaller wheel = .014m

radius of larger wheel = .15m

circumference of smaller wheel = 2*pi*r = 2*3.14*.014 = .08792

angular velocity of smaller wheel (given) = 407 rad/s

angular velocity = circumference/time

time = circumference/angular velocity

=.08792/407 = .000216s

circumference of larger wheel = 2*pi*r = 2*3.14*.15 = .942

angular velocity = circumference/time

=.942/.000216 =

**4361.11 rad/s**

Does this approach look right?