The square of an integer is a perfect square. what is the smallest perfect square that is a multiple of 2, of 4, of 6, and of 8?

144

Explanation:

This is something you can do though trial and error. Start at 8 and work your way up squaring each whole number.

8^2 = 64 is a multiple of 8, 4 and 2, but not a multiple of 6

9^2 = 81 is a multiple of neither 2,4,6,8

10^2 = 100 is a multiple of 2 and 4 but nothing else in the list

11^2 = 121 is a multiple of neither 2,4,6,8

12^2 = 144 is a multiple of all four values 2,4,6,8 as each division results in a whole number, as shown below:

144/2 = 72

144/4 = 36

144/6 = 24

144/8 = 18

Those four computations show how 144 is a multiple of 2,4,6, and 8.