What is the LCM of 30 and 40?

The Least Common Multiple (LCM) of two numbers is the smallest multiple that is evenly divisible by both numbers. To find the LCM of 30 and 40, we can use the prime factorization method.

Step 1: Prime Factorization

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

• 30 = 2 × 3 × 5
• 40 = 2 × 2 × 2 × 5 (or 2³ × 5)

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 2³
• For 3: the highest power is 3¹
• For 5: the highest power is 5¹

Step 3: Calculate the LCM

Now, we multiply these highest powers together:

LCM = 2³ × 3¹ × 5¹

Calculating this gives:

• 2³ = 8
• 3¹ = 3
• 5¹ = 5

So, LCM = 8 × 3 × 5 = 120.

Final Answer

The LCM of 30 and 40 is 120.