SOLUTION: On its first anniversary the store gave away a free gift hamper to every 75th customer and discount coupon to every 90th customer. If 1000 customers visited the store on that day t

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Question 1151886: On its first anniversary the store gave away a free gift hamper to every 75th customer and discount coupon to every 90th customer. If 1000 customers visited the store on that day then how many customers got both free gift hamper and discount voucher
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
75 has multiples that end in 5 and 0, so half of the 75 can be a multiple of 90, which has only multiples that end in 0
13*75=965, which cannot be a multiple of both, so there are only 12 multiples of 75 that can possibly work and half of them end in 5, so that leaves 6 that end in 0.
150
300
450
600
750
900
90 divides evenly into 450 and 900.
Two customers.
Answer by ikleyn(52810)   (Show Source): You can put this solution on YOUR website!
.

In accurate mathematical formulation, the question is



    In the set of integer numbers from 1 to 1000, how many integers are multiples of 75 and 90, simultaneously ?



The least common multiple of the numbers  75 = 15*5  and  90 = 15*6  is  15*5*6 = 450,

so there are exactly 2 such numbers, 450 and 900.


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