The LCM of 24, 36, 40 is .

Options

A. 4
B. 90
C. 360
D. 720

Answer

To find the LCM (Least Common Multiple) of the numbers 24, 36, and 40, we can follow these steps:

### Step 1: Find the prime factorization of each number.

- **For 24:**
- 24 = 2 × 12
- 12 = 2 × 6
- 6 = 2 × 3
- So, the prime factorization of 24 is: **2^3 × 3^1**

- **For 36:**
- 36 = 2 × 18
- 18 = 2 × 9
- 9 = 3 × 3
- So, the prime factorization of 36 is: **2^2 × 3^2**

- **For 40:**
- 40 = 2 × 20
- 20 = 2 × 10
- 10 = 2 × 5
- So, the prime factorization of 40 is: **2^3 × 5^1**

### Step 2: Identify the highest power of each prime factor.

- For the prime factor **2**, the highest power is **2^3** (from 24 and 40).
- For the prime factor **3**, the highest power is **3^2** (from 36).
- For the prime factor **5**, the highest power is **5^1** (from 40).

### Step 3: Multiply the highest powers of all prime factors together.

Now, we can calculate the LCM by multiplying these highest powers:

\[ LCM = 2^3 × 3^2 × 5^1 \]

Calculating this step by step:

1. Calculate \(2^3 = 8\)
2. Calculate \(3^2 = 9\)
3. Calculate \(5^1 = 5\)

Now multiply these results together:

\[ LCM = 8 × 9 × 5 \]

### Step 4: Perform the multiplication.

1. First, multiply \(8 × 9 = 72\)
2. Then, multiply \(72 × 5 = 360\)

### Conclusion

Thus, the LCM of 24, 36, and 40 is **360**.

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