A number is divisible by 5 and 6. It may not be divisible by
10
15
30
60
Step 1: Understand the given.
The number is divisible by 5 and by 6.
Step 2: Use LCM idea.
If a number is divisible by 5 and 6, then it is divisible by their LCM.
Prime factors: \(5 = 5\), \(6 = 2 \times 3\).
LCM \(= 2 \times 3 \times 5 = 30\).
So the number is a multiple of 30.
Write it as \(n = 30k\), where \(k\) is a whole number.
Step 3: Check each option.
For 10: \(n \div 10 = 30k \div 10 = 3k\) → an integer. So always divisible by 10.
For 15: \(n \div 15 = 30k \div 15 = 2k\) → an integer. So always divisible by 15.
For 30: \(n \div 30 = 30k \div 30 = k\) → an integer. So always divisible by 30.
For 60: \(n \div 60 = 30k \div 60 = k/2\).
\(k/2\) is not always an integer (only when \(k\) is even).
Conclusion: The number may not be divisible by 60. (Option D)