What is the Least Number Divisible by 8, 9, 10?

The least number divisible by 8, 9, and 10 is 360.

To find the least number divisible by 8, 9, and 10, we need to determine the Least Common Multiple (LCM) of these three numbers. The LCM is the smallest positive integer that is divisible by each of the given numbers.

Here's how to calculate the LCM:

1. Prime Factorization: Find the prime factorization of each number.

   • 8 = 2 x 2 x 2 = 2³
   • 9 = 3 x 3 = 3²
   • 10 = 2 x 5

2. Identify Highest Powers: Identify the highest power of each prime factor present in any of the factorizations.

   • 2³ (from 8)
   • 3² (from 9)
   • 5¹ (from 10)

3. Multiply: Multiply these highest powers together.

   • LCM(8, 9, 10) = 2³ x 3² x 5 = 8 x 9 x 5 = 360

Therefore, 360 is the smallest number that is exactly divisible by 8, 9, and 10.