What is the fastest way to gain muscle when you work out?

Squats. The squat activates the most muscles, uses the largest muscles, and takes those muscles through the longest range of motion. This stimulates the release of the largest amounts of hormones related to muscle growth, which circulate around the body and are used by all muscles being worked. So squats not only make your lower body stronger and build muscle, but they support all muscle gain from workouts in the days that follow the squats.

For someone just getting into lifting I advocate the Stronglifts 5x5 workout plan. It has a lot of advantages for someone in their first year of lifting. After that, a lifter should be experienced enough and know their body well enough to evaluate other lifting plans and begin experimenting to see what lifting schedule will take them to the next level.

EDIT: The 5 exercises Joe has given are the 5 used in the Stronglifts program, in their order of importance to your body.

1) Squat

2) Dead Lift

3) Bench Press

4) Bent over rows

5) Shoulder Press

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