What is the smallest natural number divisble bye 2,4,6,and 8?

Question

also if you could help me with these:

A rectangular region of state forest land has an area of 80 square miles. The length and the width are natural numbers. Find the possible dimensions.

A rancher wants to fence in a corrall for his prize winning stallion. he wishes to have an area of 400 square yards. He also wants the perimeter to be as small as possible in order to minimize the cost of the fencing. If the side lengths are natural numbers,find dimensions of the corral.

Answer 1

2, 4, 6, and 8 all go into 24.

Answer 2

main question

Take LCM of 2,4,6,8 it is 24.

A rectangular region... :Factorize 80 we get 2x2x2x2x5, now take all combinations of lengths and breadths for example, 2x2 and 2x2x5 i.e. 4 and 20

like wise take all combinations by dividing the factors into twp groups.

A rancher wants to..:

Factorize 400 we get 2x2x2x2x5x5

now take all combinations in two groups to find Length (l) and Breadth (b) of corral,

from the combinations take the one which gives minimum of 2(l+b) value

Its 16 and 25 i guess.

Answer 3

24 is the smallest & idk bout the other ones sorry =[