Question #93564
A pro baseball team is having a promotion in which every tenth fan that enters the stadium gets a free hat and every 12th person gets a free t shirt. How many fans will come into the stadium before a fan receives a hat and a t shirt?
1
Expert's answer
2019-09-02T09:14:09-0400

If a fan receives a hat and a T-shirt, then his number is divisible by 10 and 12. Therefore, this number is the least common multiple of 10 and 12.

Prime factorizations of 10 and 12 are:

10=2510=2\cdot 5

12=22312=2\cdot2\cdot3.

LCM is the product of maximum occurrences of each prime factor in the given numbers.

LCM(10,12)=2235=60LCM(10,12)=2\cdot2\cdot3\cdot5=60

Hence, 59 fans will come into the stadium before the 60th fan receives a hat and a T-shirt.



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