What is the least number exactly divisible by 6, 9, 15 and 20?

The least number exactly divisible by 6, 9, 15, and 20 is 180. This is also known as the Least Common Multiple (LCM).

Finding the Least Common Multiple (LCM)

To find the LCM of 6, 9, 15, and 20, we can use the prime factorization method:

1. Prime Factorization of Each Number:

   • 6 = 2 x 3
   • 9 = 3 x 3 = 3²
   • 15 = 3 x 5
   • 20 = 2 x 2 x 5 = 2² x 5

2. Identify the Highest Power of Each Prime Factor:

   • 2² (from 20)
   • 3² (from 9)
   • 5 (from 15 or 20)

3. Multiply the Highest Powers Together:

   • LCM = 2² x 3² x 5 = 4 x 9 x 5 = 180

Therefore, the least number exactly divisible by 6, 9, 15, and 20 is 180.