\div 30 = 12
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- Solution: To find the smallest number of samples per column such that the number of columns is a multiple of both 6 and 10, we compute the least common multiple (LCM) of 6 and 10:
- \text{LCM}(6, 10) = \text{LCM}(2 \times 3, 2 \times 5) = 2 \times 3 \times 5 = 30
- So there must be at least 30 columns. To minimize the number of samples per column, we use the smallest number of columns that satisfies the condition, which is 30. Then the number of samples per column is:
- Thus, the smallest number of samples per column is
- $$Question: Find the minimum value of $(\cos x + \sec x)^2 + (\sin x + \csc x)^2$.
- Using identities $\cos x \sec x = 1$ and $\sin x \csc x = 1$, this simplifies to:
