What is the least common multiple of 36 and 54?

To find the least common multiple (LCM) of 36 and 54, we can use the prime factorization method.

Step 1: Prime Factorization

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

• 36: 2 × 2 × 3 × 3 (or 2² × 3²)
• 54: 2 × 3 × 3 × 3 (or 2¹ × 3³)

Step 2: Identify the Highest Powers

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

• For 2: the highest power is 2²
• For 3: the highest power is 3³

Step 3: Calculate the LCM

Now, we multiply these together to find the LCM:

LCM = 2² × 3³ = 4 × 27 = 108

Final Answer

The least common multiple of 36 and 54 is 108.