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?

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Mathematics

9 March, 16:36

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?

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Answers (1)

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Nathaniel Gibbs · 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