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15 December

The arithmetic mean of a set of n numbers is computed by adding up all the numbers, then dividing the result by n. The geometric mean of a set of n numbers is computed by multiplying all the numbers together, then taking the nth root of the result.
The arithmetic mean of the digits of the number 132 is 13(1+3+2)=2. The geometric mean of the digits of the number 139 is 1×3×93=3.
What is the smallest three-digit number whose first digit is 4 and for which the arithmetic and geometric means of its digits are both non-zero integers?

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