Wheeling Along

One wheel has circumference of 3 feet, and a second wheel has circumference of 4ft. The smaller wheel starts rolling first, and the larger wheel begins rolling after the smaller wheel has gone around x number of times. The larger wheel rolls 2.8 times as fast as the smaller wheel and will eventually catch up with the wheel. If the larger wheel catches up with the smaller wheel in an integral number of revolutions, then what is the smallest value of x? Justify your answer.

(Source: Adapted from Mathematics Teaching in the Middle School, Apr 1994)