Find the LCM of: 4, 5, and 6.

To find the least common multiple (LCM) of the numbers 4, 5, and 6, we can follow a systematic approach.

Step 1: Identify the Prime Factors

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

• 4 = 2 × 2 (or 2²)
• 5 = 5 (itself, since 5 is prime)
• 6 = 2 × 3

Step 2: Determine the Highest Powers

Next, we take the highest power of each prime number that appears in the factorizations:

• 2 appears as 2² (from 4)
• 3 appears as 3¹ (from 6)
• 5 appears as 5¹ (from 5)

Step 3: Calculate the LCM

Now, we multiply these highest powers together:

LCM = 2² × 3¹ × 5¹

Calculating this gives:

• 2² = 4
• 4 × 3 = 12
• 12 × 5 = 60

Final Result

The least common multiple of 4, 5, and 6 is 60.