The autonomous operation of small quadcopters moving at high speed in an unknown cluttered environment is a challenging task. Current works in the literature formulate it as a Sense-And-Avoid (SAA) problem and address it by either developing new sensing capabilities or small form-factor processors. However, the SAA, with the high-speed operation, remains an open problem. The significant complexity arises due to the computational latency, which is critical for fast-moving quadcopters. In this paper, a novel Fast Obstacle Avoidance Motion (FOAM) algorithm is proposed to perform SAA operations. FOAM is a low-latency perception-based algorithm that uses multi-sensor fusion of a monocular camera and a 2-D LIDAR. A 2-D probabilistic occupancy map of the sensing region is generated to estimate a free space for avoiding obstacles. Also, a local planner is used to navigate the high-speed quadcopter towards a given target location while avoiding obstacles. The performance evaluation of FOAM is evaluated in simulated environments in Gazebo and AIRSIM. Real-time implementation of the same has been presented in outdoor environments using a custom-designed quadcopter operating at a speed of $4.5$ m/s. The FOAM algorithm is implemented on a low-cost computing device to demonstrate its efficacy. The results indicate that FOAM enables a small quadcopter to operate at high speed in a cluttered environment efficiently.