Question

Every fourth visitor to a museum gets a free bumper sticker.Every tenth visitor to that museum gets a free key chain.Which ordered visitor will be the first one to get both the bumper sticker and the chain?

Answer 1

You have to use least common multiple so that's going to be
4-8-12-16-20
10-20
The 20th person gets both first

Answer 2

The
`20^(th)` visitor will get both a bumper sticker and free key chain.

Explanation:

We are given the following information in the question:

Every
`4^(th)` visitor gets a bumper ticket in the museum.

Also, every
`10^(th)` visitor gets a free key chain.

We have to find a visitor that will get both the bumper ticket and the free key chain.

This can be done by finding Lowest common multiple(LCM) of 4 and 10.

Lowest common multiple of 4 and 10 is smallest possible number that is divisible by both 4 and 10.

We can do this with the help of prime factorization.

`4 = 2* 2`

`10 = 2* 5`

`\bold{LCM} = 2* 2* 5 = 20`

Hence, the
`20^(th)` visitor will get both a bumper sticker and free key chain.