Each of the small letters in bold represents a different base 36 digit from 0 to Z to satisfy this cryptarithmetic equation. None of the numbers can contain any leading zero.

ab.c + b.cd = (ab.c)*(b.cd)

Prove that abc is always divisible by bcd.

Note: Adjacent numerals are multi-digit base 36 numbers, and not the product. For example, if a=1, b=2, c=3 and d=4, then b.cd represents the base-36 number 2.34 and, a.bc represents the base 36 number 1.23.