A movie rental store gives a free popcorn to every 35th customer and a free movie rental to every 45th customer. Which customer was the first to win both prizes?

Answer 1

35 x 45 = 1575th customer wins both, but because 35 and 45 are both divisible by 5, there should be an earlier customer who also wins both.

35 = 5x7

45=5x9

least common multiple is 5x7x9 = 315. The 315th customer is 1st to win both prizes

35 45

70 90

105 135

140 180

175 225

210 270

245 315

280

315

there's 2 arithmetic sequences, and 315 is the 1st time they have the same term