math reasoning:need help

Why does any 3-digit number when multiplied by 7, and the result is
multiplied by 11 and the second result is multiplied by 13, gives the
original number 2 times?
For example, 112 is the original 3 digit number.
112*7= 784
784*11=8624
8624*13=112 112.
Please tell me why it happens with all 3 digit number? and why it is
only happen when multiplied by7,11 and 13( all of these are prime
numbers).
.