the answer is 60 but im going to explain it down below if you want to know how to do it :)
first because we dont know the values of the 6 numbers we have to lay it out like this.
x
x+2
x+4
x+6
x+8
x+10
-------- (then we add it together)
6x+30 = 390 (the sum of the 6 numbers)
using this equation we find out what x is
so we do 390-30 to find what 6x is, which is 360
because now we know that 6x=360, we divide 360 by 6 to find out what x is
360 divided by 6 =60..... x = 60
so now we know that the smallest integer is 60
to check the answer we could add the 6 numbers which are:
60+62+64+66+68+70=390 :)
so the smallest integer is 60