What is the least common multiple of 6, 9 and 10?

To find the least common multiple (LCM) of the numbers 6, 9, and 10, we can follow a systematic approach.

Step 1: Prime Factorization

First, we break down each number into its prime factors:

• 6 = 2 × 3
• 9 = 3 × 3 (or 3²)
• 10 = 2 × 5

Step 2: Identify Unique Factors

Next, we list all the unique prime factors, taking the highest power of each:

• 2 (from 6 and 10)
• 3² (from 9)
• 5 (from 10)

Step 3: Calculate the LCM

Now, we multiply these factors together:

LCM = 2 × 3² × 5

Calculating this gives:

• 2 × 9 = 18
• 18 × 5 = 90

Final Result

The least common multiple of 6, 9, and 10 is 90.