Find the LCM of 216 and 240.

To find the Least Common Multiple (LCM) of 216 and 240, we can use the prime factorization method. Here’s how it works:

Step 1: Prime Factorization

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

• 216: 2 × 2 × 2 × 3 × 3 = 2³ × 3²
• 240: 2 × 2 × 2 × 2 × 3 × 5 = 2⁴ × 3¹ × 5¹

Step 2: Identify the Highest Powers

Next, we take the highest power of each prime factor from both factorizations:

• For 2: the highest power is 2⁴
• For 3: the highest power is 3²
• For 5: the highest power is 5¹

Step 3: Calculate the LCM

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

LCM = 2⁴ × 3² × 5¹

Calculating this gives:

• 2⁴ = 16
• 3² = 9
• 5¹ = 5

Now, multiply them together:

LCM = 16 × 9 × 5 = 720

Final Result

The Least Common Multiple of 216 and 240 is 720.