# Logical Number Theory

**Number Theory**Level 4

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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