What is the smallest number divisible by each of 9, 12, and 15?

The smallest number divisible by each of 9, 12, and 15 is 180. This is also known as the Least Common Multiple (LCM).

To find the LCM, we can use the prime factorization method:

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

   • 9 = 3 x 3 = 3²
   • 12 = 2 x 2 x 3 = 2² x 3
   • 15 = 3 x 5

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

   • 2²
   • 3²
   • 5

3. Multiply the Highest Powers: Multiply these highest powers together:

   • 2² x 3² x 5 = 4 x 9 x 5 = 180

Therefore, the Least Common Multiple (LCM) of 9, 12, and 15 is 180. This means that 180 is the smallest number that can be divided evenly by 9, 12, and 15.