Logical Number Theory

Each alphabet is represented as a number as shown in the image above. So now you choose an arbitrary word and represent it in the form of numbers above and let $$P$$ be the product of these numbers.

Find the smallest three digit composite number which cannot take the value of $$P$$ for any arbitrary word.

Details And assumptions:

• You can choose any word (whether it makes sense or not does not matter).

• As an explicit example , if the word is $$nihar$$ , then $$P=14\times 9 \times 8 \times 1 \times 18 = 18144$$.

• This problem is original.

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