To solve this problem, we need to analyze the divisibility properties of a number that is divisible by both 5 and 6.

Key Insights:

1. Divisibility by 5 and 6 implies that the number is divisible by the Least Common Multiple (LCM) of 5 and 6.

   • LCM(5, 6) = $30$. Hence, the number must be divisible by 30.

2. For divisibility by the given options, let's check:

   • (a) 10: A number divisible by 30 is divisible by 10, as 30 is a multiple of 10.
   • (b) 15: A number divisible by 30 is divisible by 15, as 30 is a multiple of 15.
   • (c) 30: By definition, the number is divisible by 30.
   • (d) 60: A number divisible by 30 may or may not be divisible by 60, depending on whether it contains an additional factor of 2 (since $60 = 30 \times 2$).

Conclusion:

The correct answer is (D) 60, as the number may not be divisible by 60.

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Would you like further explanation or help with related concepts? Here are five questions for exploration:

1. What is the LCM, and how is it calculated?
2. Why is divisibility by a number related to its factors?
3. How does the presence of additional factors (like 2 in 60) change divisibility rules?
4. What are some real-life applications of divisibility and LCM?
5. How can prime factorization help with divisibility questions?

Tip: When solving divisibility problems, always consider the LCM to simplify the calculations and reasoning.