The manager of a store wants to have a sales promotion where she gives prizes to the first several people through the door. The manager wants each person to receive the exact same items and in the same amount. She also wants to distribute all of the prizes. The manager has 240 pins, 360 ornaments, and 540 mugs to distribute.
How many people will get gifts? @History

Question

The manager of a store wants to have a sales promotion where she gives prizes to the first several people through the door. The manager wants each person to receive the exact same items and in the same amount. She also wants to distribute all of the prizes. The manager has 240 pins, 360 ornaments, and 540 mugs to distribute.
How many people will get gifts?   @History

anonymous · Answer

GCD( 240, 360, 540 ) = 60$$\left(\frac{1}{60}\right)\{240,360,540\}=\{4,6,9\} $$Each person through the door will receive 4, 6 and 9 each pins, ornaments and mugs respectively which will be exhausted after the 60th person.