Which one of the following number is divisible by 5 and 6 both?

To find which number is divisible by both 5 and 6, we need to determine the least common multiple (LCM) of 5 and 6. The LCM of two numbers is the smallest number that is divisible by both.

1. The prime factorization of 5 is: \( 5^1 \)
2. The prime factorization of 6 is: \( 2^1 \times 3^1 \)

To get the LCM, we take the highest powers of all prime factors involved:

\[
\text{LCM}(5, 6) = 2^1 \times 3^1 \times 5^1 = 30
\]

Thus, any number divisible by both 5 and 6 must be divisible by 30. If you're given a list of numbers, you should check which one is divisible by 30.

If you provide a list, I can help identify the correct number.

Would you like more details or have any further questions? Here are five related questions for exploration:

1. How do you calculate the LCM for other numbers?
2. Can a number be divisible by 5 but not 6?
3. How can you quickly identify if a number is divisible by 5 or 6?
4. What is the difference between GCD and LCM?
5. What are some other common divisibility rules?

**Tip:** A number divisible by 5 will always end in 0 or 5!

Discover how to determine if a number is divisible by both 5 and 6 using the Least Common Multiple (LCM). This solution explains the LCM of 5 and 6, the prime factorization approach, and provides tips on divisibility rules. Ideal for middle school students learning number theory and divisibility.

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