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Prime factors are the basic building blocks of numbers. Any number greater than 1 can be broken down into these building blocks, which are called prime factors. A prime factor is a prime number that can divide the given number exactly, leaving no remainder.
For instance, the prime factors of 12 are broken down as 2, 2 and 3 because 12 can be expressed as the product of these primes: \( 12 = 2 \times 2 \times 3 \).
Similarly, for 15, the prime factors are 3 and 5 because 15 = 3 x 5.
Learning to determine the prime factors of a number will help you in more advanced topics in math, such as finding the Least Common Multiple (LCM).

The Least Common Multiple (LCM) is the smallest positive number that is evenly divisible by all the numbers in a given set. To determine the LCM, we combine the highest powers of all the prime factors from each number.
For instance, if we need to find the LCM of 5, 12, and 15, we first find their prime factors:
- 5: 5
- 12: 2, 2, 3
- 15: 3, 5
Next, we identify the highest power of each prime factor in the list. For example:
- The highest power of 2 is \( 2^2 \) from 12
- The highest power of 3 is \( 3^1 \) from both 12 and 15
- The highest power of 5 is \( 5^1 \) from both 5 and 15
Then we multiply these highest powers together to find the LCM:
\( LCM = 2^2 \times 3^1 \times 5^1 = 4 \times 3 \times 5 = 60 \).

Let's break down the process step by step to find the LCM of a set of numbers:

**Step 1: Find the prime factors**
Determine the prime factors of each number. For 5, the prime factors are: 5. For 12, they are: 2, 2, 3 (since 12 = 2 × 2 × 3). And for 15, the prime factors are: 3, 5 (since 15 = 3 × 5).

**Step 2: Identify the highest power of each prime factor**
List the highest powers of all the prime numbers found in Step 1. The prime numbers we have are 2, 3, and 5. The highest power of 2 is \( 2^2 \) (from 12). The highest power of 3 is \( 3^1 \) (from both 12 and 15). The highest power of 5 is \( 5^1 \) (from both 5 and 15).

**Step 3: Calculate the LCM**
Multiply the highest powers of each prime factor together: \( LCM = 2^2 \times 3^1 \times 5^1 \). This gives us \( LCM = 4 \times 3 \times 5 = 60 \).