交大110 線性代數與離散數學第3題｜離散數學 Ch1 集合與基礎數論

離散數學›Ch1 集合與基礎數論

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8. 最大公因數、最小公倍數、基礎數論

#LS-01-008中最大公因數最小公倍數基礎數論

(5 points) Assume $n \ge 2$ . Let $A = \{x_1, x_2, \ldots, x_n\}$ be a set of (not necessarily distinct) natural numbers. Let $g = \gcd(x_1, x_2, \ldots, x_n)$ and $l = \text{lcm}(x_1, x_2, \ldots, x_n)$ . Assume $n$ , $g$ , and $l$ are appropriate fixed integers. Let $p = x_1 \cdot x_2 \cdot \ldots \cdot x_n$ , the product of $x_i$ 's. What is the largest possible value of $p$ in terms of $n$ , $g$ , and $l$ ? What is the smallest possible value of $p$ in terms of $n$ , $g$ , and $l$ ?

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