Find the least number that is divisible by first five even numbers.

Answer

To find the least number that is divisible by the first five even numbers, we need to determine the Least Common Multiple (LCM) of the numbers 2, 4, 6, 8, and 10. Here’s the step-by-step solution:

### Step 1: Identify the first five even numbers
The first five even numbers are:
- 2
- 4
- 6
- 8
- 10

### Step 2: Find the prime factorization of each number
- **2** = 2
- **4** = 2²
- **6** = 2 × 3
- **8** = 2³
- **10** = 2 × 5

### Step 3: Determine the highest power of each prime factor
Now, we will take the highest power of each prime factor from the factorizations:
- The highest power of **2** among the numbers is **2³** (from 8).
- The highest power of **3** is **3¹** (from 6).
- The highest power of **5** is **5¹** (from 10).

### Step 4: Calculate the LCM using the highest powers
The LCM is found by multiplying the highest powers of all prime factors:
\[ \text{LCM} = 2^3 \times 3^1 \times 5^1 \]

Calculating this step-by-step:
- \(2^3 = 8\)
- \(3^1 = 3\)
- \(5^1 = 5\)

Now multiply these together:
\[ \text{LCM} = 8 \times 3 \times 5 \]

Calculating:
1. \(8 \times 3 = 24\)
2. \(24 \times 5 = 120\)

### Step 5: Conclusion
Thus, the least number that is divisible by the first five even numbers (2, 4, 6, 8, and 10) is **120**.