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**"Find the smallest square number that is divisible by each of the numbers 4, 9, and 10."**

### Let's solve this step-by-step:

1. **Prime factorization**:
   - 4 = \( 2^2 \)
   - 9 = \( 3^2 \)
   - 10 = \( 2 \times 5 \)

2. **LCM (Least Common Multiple)**:
   To find the smallest square number divisible by 4, 9, and 10, first we need the LCM of these numbers. We take the highest powers of all the primes involved.
   - The prime factors involved are 2, 3, and 5.
   - The highest power of 2 is \( 2^2 \) (from 4).
   - The highest power of 3 is \( 3^2 \) (from 9).
   - The highest power of 5 is \( 5 \) (from 10).

   So, the LCM is:
   \[
   LCM(4, 9, 10) = 2^2 \times 3^2 \times 5 = 180
   \]

3. **Make the LCM a perfect square**:
   For the LCM to be a square number, every prime factor must have an even exponent. Right now, we have \( 2^2 \times 3^2 \times 5^1 \), and the exponent of 5 is odd. To make it even, we need to multiply by one more factor of 5.

   Therefore, the smallest square number divisible by 4, 9, and 10 is:
   \[
   180 \times 5 = 900
   \]

### Final answer: **900**

Would you like further details on this solution or a breakdown of any specific steps? 

Here are some related questions for practice:
1. What is the LCM of 6, 15, and 20?
2. Find the smallest cube number divisible by 6, 8, and 12.
3. How do you find the smallest square number divisible by 7 and 14?
4. What is the prime factorization of 180?
5. How do you determine if a number is a perfect square?

**Tip**: Always check the exponents of prime factors when finding the smallest square or cube numbers!

Find the smallest square number that is divisible by each of the numbers 4, 9, and 10.

Learn how to find the smallest square number divisible by 4, 9, and 10. This problem involves prime factorization, least common multiple (LCM), and understanding the properties of square numbers. Suitable for students in Grades 8-10.

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