Solution

(related to Problem: Digital Multiplication)

The solution that gives the smallest possible sum of digits in the common product is $23 \times 174 = 58 \times 69 = 4,002,$ and the solution that gives the largest possible sum of digits, $9 \times 654 = 18 \times 327 = 5,886.$ In the first case, the digits sum to $6$ and in the second case to $27.$ There is no way of obtaining the solution but by actual trial.

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References

Project Gutenberg

1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

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