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Omni-MATH / Let S be the set of all positive factors of 6000. What is the probability of a random quadruple (a,b,c,d)∈S⁴ satisfies …

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problem

Let SS be the set of all positive factors of 6000. What is the probability of a random quadruple (a,b,c,d)∈S4(a, b, c, d) \in S^{4} satisfies $$\operatorname{lcm}(\operatorname{gcd}(a, b), \operatorname{gcd}(c, d))=\operatorname{gcd}(\operatorname{lcm}(a, b), \operatorname{lcm}(c, d)) ?$$
Plain-text mathematical notation (without MathML)
Let S be the set of all positive factors of 6000. What is the probability of a random quadruple (a,b,c,d)∈S⁴ satisfies $$\operatorname{lcm}(\operatorname{gcd}(a, b), \operatorname{gcd}(c, d))=\operatorname{gcd}(\operatorname{lcm}(a, b), \operatorname{lcm}(c, d)) ?$$
Original LaTeX notation
Let $S$ be the set of all positive factors of 6000. What is the probability of a random quadruple $(a, b, c, d) \in S^{4}$ satisfies $$\operatorname{lcm}(\operatorname{gcd}(a, b), \operatorname{gcd}(c, d))=\operatorname{gcd}(\operatorname{lcm}(a, b), \operatorname{lcm}(c, d)) ?$$

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task_id
44f221b9-efe5-5e66-826f-529c979ee1a7
task_key
test--44f221b9-efe5-5e66-826f-529c979ee1a7
task_revision_id
1
config / split
/ test

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