All the numbers here are octal.
$(12345)×(54321) = (d17743365)$
Is there an efficient way to find missing digit $d$ without hard multiplication? I could have used $ \mod9$ congruency if it was decimal, but I am finding hard time figuring out the same technique for octal base.
If you express any number $m$ in octal and you get $d_nd_{n-1}\ldots d_1d_0$, then$$m\equiv d_0-d_1+d_2-\cdots(-1)^nd_n\pmod 9.$$So, both $12\,345_8$ and $54\,321_8$ are congruent to $3\pmod 9$, and therefore their product is congruent to $0\pmod9$. And the only $d$ that will work there is $7$:$$7\overbrace{-1+7-7-4+3-3+6-5}^{\phantom{2}=2}=9\equiv0\pmod9.$$