Q6Discrete Mathematics Structure

In the poset $(S,/)$ where $/$ is 'divides':

• LUB({2, 9}): We need the smallest element $x\in S$ such that $2|x$ and $9|x$. The LCM of 2 and 9 is 18. Since $18\in S$, LUB = 18.
• GLB({60, 72}): We need the largest element $y\in S$ such that $y|60$ and $y|72$. The GCD of 60 and 72 is 12. Since $12\in S$, GLB = 12.