The most efficient way to lose weight from working out are high rep/low weight circuit training and through HIIT (high intensity interval training). Your goal should be to increase metabolism and fat burning potential throughout the day. Both HIIT and circuit weight training are both effective. To be maximized you should exercise for 1 hour 5-6 times a week. You could alternate between cardio days and circuit training days. Here is an example. 

Mon: HIIT

Tues: Circuit training

Wed: rest Thurs: HIIT

Fri: Circuit training

Sat: HIIT

Sun: Rest  

Here is an example of a circuit and  HIIT Circuit. 15-20 reps 1 minute rest between sets. Repeat for 20-30 minutes. (feel free to use the template and build your own) Upper: pushups Lower: Squats Core: Crunches Plyo: Burpees Upper: Clean and press or curl to press Lower: Alternating weighted lunges Core: Reverse crunches Plyo: Step ups    HIIT (can be done on almost any cardio machine) 3 minute warmup -30 second sprint  -1 minute recovery *Repeat for 15 minutes to 30 minutes* 3 minute cool down Top fat loss mistakes for cardio and weight training Cardio: Doing 1 speed with no resistance cardio. This kills me. Your fat burning potential begins and ends when you do. If it doesn't challenge you it will not change you. Atleast put the resistance on mountain or random.  Weight: Resting too long in between sets. Super sets are key here. Work one set while resting the other. Example of a superset is chest press and seated row together. Quad machine and ham machine. Pullup and shoulder press.  When you ramp up your metabolism you are going to have to eat more. Losing weight isn't about calories. Losing weight is about nutrient density.