If a motor has a speed of 1500 rpm, how could we reduce its speed to 300 rpm?

Here, you have not specified whether it is an AC motor or a DC
motor you are talking about.

For a DC motor the speed of the motor
can be controlled by changing the input voltage. If the motor is designed to rotate at 1500 rpm
for a voltage Vmax, if we apply a voltage Vmax/5, the angular velocity becomes 1/5 and is equal
to 300 rpm.

An AC motor's speed is more difficult to control and the
way is dependent on what type of AC motor we are referring to.

For
both the motors, the angular speed can also be altered with the use of gears. In this case we
would need two gears, one with X spokes fixed at the shaft of the motor and a gear linked to this
gear and which has 5X spokes rotates at 300 rpm.