What is the least number divisible by 15, 20, and 30?

The least number divisible by 15, 20, and 30 is 60. This number is also known as the Least Common Multiple (LCM) of 15, 20, and 30.

Here's how to find the LCM:

1. Prime Factorization:

• 15 = 3 x 5
• 20 = 2 x 2 x 5 = 2² x 5
• 30 = 2 x 3 x 5

2. Identify the Highest Powers of All Prime Factors:

• 2² (from 20)
• 3 (from 15 and 30)
• 5 (from 15, 20, and 30)

3. Multiply the Highest Powers:

LCM (15, 20, 30) = 2² x 3 x 5 = 4 x 3 x 5 = 60

Therefore, 60 is the smallest number that is divisible by 15, 20, and 30 without leaving a remainder.