The smallest number which is divisible by 12,16,18,21 and 28 is LCM of these numbers.
12 = 2x2x3
16 = 2x2x2x2
18 = 2x3x3
21 = 3x7
28 = 2x2x7
LCM(12,16,18,21, 28) = 2x2x2x2x3x3x7 = 1008
1008 + 7 = 1015
Hence the required number is 1015. If we diminish by 7, It will be divisible by 12,16,18,21 and 28.