What is the least perfect square divisible by 8, 9 and 10?

Sure, let's solve this step by step:

1. First, we need to find the least common multiple (LCM) of 8, 9, and 10. The prime factorization of 8 is 2^3, of 9 is 3^2, and of 10 is 2*5. So, the LCM is 2^3 * 3^2 * 5 = 360.

2. Now, we need to make this number a perfect square. A perfect square has all prime factors to an even power. Here, 2 and 3 are already to an even power, but 5 is to the power of 1. So, we multiply 360 by 5 to get 1800.

3. Therefore, the least perfect square divisible by 8, 9, and 10 is 1800.

To find the least perfect square divisible by 8, 9, and 10, we first need to find the least common multiple (LCM) of these numbers.

Step 1: Prime factorization of the numbers

• 8 = 2^3
• 9 = 3^2
• 10 = 2*5

Step 2: Find the LCM The LCM is found by multiplying the highest power of all prime numbers that appear in the factorization of each number. So, LCM = 2^3 * 3^2 * 5 = 360

Step 3: Find the least perfect square divisible by the LCM The least perfect square divisible by the LCM is found by making all the powers of the prime factors even (since a perfect square has even powers for all its prime factors). In the LCM, the power of 5 is 1, which is not even. So, we multiply the LCM by 5 to make the power of 5 even.

So, the least perfect square divisible by 8, 9, and 10 is 360 * 5 = 1800.