Question

A store runs a promotion in which every 500 th 

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

Answer 1

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