Let the numbers be 4x, 11x and 23x.
Then, their L.C.M. = 1012x.
So, 1012x = 3036 or x = 3.
The numbers are (4 x 3), (11 x 3) and (23 x 3).
Hence, required H.C.F. = 3.

Its wrong. LCM * HCF = product of numbers is only valid for 2 numbers.
Consider an example for no 2,15,20;
LCM=2*2*3*5=60
while HCF of these two numbers is 1.
Now as per your logic LCM*HCF=product of 2 numbers
hence as per this:
60*1=2*15*20
60!=600
Hence your logic is invalid please help regarding that...!!!