What is the LCM of 8, 12, 18 and 24?

To find the least common multiple (LCM) of the numbers 8, 12, 18, and 24, we can use the prime factorization method.

Step 1: Prime Factorization

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

• 8: 2 × 2 × 2 (or 2³)
• 12: 2 × 2 × 3 (or 2² × 3)
• 18: 2 × 3 × 3 (or 2 × 3²)
• 24: 2 × 2 × 2 × 3 (or 2³ × 3)

Step 2: Identify the Highest Powers

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

• For 2, the highest power is 2³ (from 8 and 24).
• For 3, the highest power is 3² (from 18).

Step 3: Calculate the LCM

Now, we multiply these highest powers together to find the LCM:

LCM = 2³ × 3² = 8 × 9 = 72

Final Result

The least common multiple of 8, 12, 18, and 24 is 72.