**Finding the Least Common Multiple (LCM) of the First Five Natural Numbers**

To find the least positive integer that is divisible by the first five natural numbers (1, 2, 3, 4, 5), we need to determine their least common multiple (LCM). The LCM is the smallest multiple that two or more numbers have in common.

**Step 1: Prime Factorization**

We begin by finding the prime factorization of each of the five natural numbers:

- 1: Prime factorization of 1 is 1.
- 2: Prime factorization of 2 is 2.
- 3: Prime factorization of 3 is 3.
- 4: Prime factorization of 4 is 2^2.
- 5: Prime factorization of 5 is 5.

**Step 2: Identify Common Factors**

Next, we identify the common prime factors among the numbers. In this case, the only common prime factor is 2, which appears as a factor in the prime factorization of 4.

**Step 3: Determine the LCM**

To find the LCM, we take the highest power of each prime factor that appears in the prime factorizations:

- 2: The highest power of 2 is 2^2 = 4.
- 3: There is no additional power of 3.
- 5: There is no additional power of 5.

Multiplying these highest powers together, we get LCM = 2^2 * 3 * 5 = 4 * 3 * 5 = 60.

Therefore, the least positive integer that is divisible by the first five natural numbers (1, 2, 3, 4, 5) is 60.

To summarize the steps:

1. Prime factorize each of the numbers.
2. Identify the common factors among the prime factorizations.
3. Take the highest power of each common factor.
4. Multiply these highest powers together to find the LCM.

In this case, the LCM is 60, which is the smallest multiple that is divisible by 1, 2, 3, 4, and 5.

60