Let x be the first even number. Then adding 2 consecutively gives us the subsequent even numbers. That is
[tex]x,x+2,x+4,x+6[/tex]
From the question, the mean of these four numbers is 15. That is;
[tex]\frac{\sum x}{n} =15[/tex]
[tex]\Rightarrow \frac{x+(x+2)+(x+4)+(x+6)}{4} =15[/tex]
[tex]\Rightarrow \frac{x+x+2+x+4+x+6}{4} =15[/tex]
[tex]\Rightarrow \frac{x+x+x+x+2+4+6}{4} =15[/tex]
[tex]\Rightarrow \frac{4x+12}{4} =15[/tex]
Multiply both sides by 4 to obtain,
[tex]\Rightarrow 4\times \frac{4x+12}{4} =4 \times15[/tex]
[tex]\Rightarrow 4x+12 =60[/tex]
[tex]\Rightarrow 4x =60-12[/tex]
[tex]\Rightarrow 4x =48[/tex]
Divide both sides by 4 to obtain,
[tex]x =12[/tex]
Hence the greatest of the numbers is [tex]12+6=18[/tex]
and the least of the numbers is [tex]12[/tex].
