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Omni-MATH / The set of {1,2,3,...,63} was divided into three non-empty disjoint sets A,B. Let a,b,c be the product of all numbers in each set A,B,C respectively and finally we have determined …

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problem

The set of {1,2,3,...,63}\{1,2,3,...,63\} was divided into three non-empty disjoint sets A,BA,B. Let a,b,ca,b,c be the product of all numbers in each set A,B,CA,B,C respectively and finally we have determined the greatest common divisor of these three products. What was the biggest result we could get?
Plain-text mathematical notation (without MathML)
The set of {1,2,3,...,63}  was divided  into three non-empty disjoint sets A,B. Let a,b,c be the product of all numbers in each set A,B,C respectively  and finally we have determined the greatest common divisor of these three products. What was the biggest result we could get?
Original LaTeX notation
The set of $\{1,2,3,...,63\}$  was divided  into three non-empty disjoint sets $A,B$. Let $a,b,c$ be the product of all numbers in each set $A,B,C$ respectively  and finally we have determined the greatest common divisor of these three products. What was the biggest result we could get?

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