Question

There are 75 houses in the troll's street. If in every 4th house there is a pink troll, a blue troll in every 6th house and a yellow troll in every 8th house, then in how many houses are there all of pink, blue and yellow trolls?

Answer 1

3 houses have all pink, blue, and yellow.

Answer 2

The answer is 3 houses.

Explanation:

This question is based on the Least Common Multiple (LCM) method. We will find the LCM of the numbers 4, 6 and 8.

4 = 2 x 2 =
`2^(2)`

6 = 2 x 3 = 2 x 3

8 = 2 x 2 x 2 =
`2^(3)`

So, LCM is =
`2^(3)*3=24`

Therefore, at every 24th houses, we will find all three trolls colors.

And 24 is the number of houses we will find all color trolls. Then in a group of 75 houses, it will occur thrice and at every 24th place. Means. 3 houses will have all color trolls.