A store runs a promotion in which every 500th customer (500th, 1000th, 1500th, ...) received a free gift, every 800th (800th, 1600th, ...) customer receives a voucher, and every 1200th (1200th, 2400th, ...) customer receives a discount. Which lucky customer will be the first to receive all three promotional prizes?

The answer is 12,000

To solve this question, you have to find the least common multiple of the three promotional prizes. The factor of 500, 800 and 1200 would be:

500 = 2*2*5*5*5 = 2^2 * 5^3

800 = 2*2*2*2*2*5*5 = 2^5 * 5^2

1200 = 2*2*2*2*3*5*5 = 2^4 * 3 * 5^2

The LCM of those three number would be: 2^5 * 3 * 5^3 = 12,000