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Prime factorization is a method used to break down a number into its smallest divisible prime factors. It is like finding the building blocks of a number. For example, to find the prime factors of 12, start by dividing it by the smallest prime number which is 2.
12 ÷ 2 = 6
Next, continue dividing by 2: 6 ÷ 2 = 3.
Finally, 3 is already a prime number. So, the complete prime factorization of 12 is 2² * 3.
Similarly, for 20, start by dividing by 2: 20 ÷ 2 = 10, then 10 ÷ 2 = 5.
Since 5 is a prime number, the prime factorization of 20 is 2² * 5.
It's essential to understand prime factorization as it forms the foundation for calculating the least common multiple (LCM) in further steps.

The Least Common Multiple (LCM) of two numbers is the smallest number that is divisible by both of them. We use the prime factorization of each number to help find the LCM.
After performing prime factorization on the numbers, list all the prime factors. For the numbers 12 and 20, the prime factors are:
- For 12: 2² and 3
- For 20: 2² and 5
To find the LCM, you need the highest power of each prime number appearing in either factorization.
- Maximum power of 2: 2²
- Maximum power of 3: 3¹
- Maximum power of 5: 5¹
By combining these highest powers, you can correctly find the LCM.

Let's put everything together and walk through the mathematical steps to calculate the LCM using our factorizations.
1. List all the highest powers of prime factors from both numbers. In our case: 2², 3¹, and 5¹.
2. Multiply these highest powers together to find the LCM.
3. Substituting in our values:
\[ \text{LCM} = 2² \times 3¹ \times 5¹ \]
4. Performing the multiplication step-by-step:
\[ 2² = 4 \]
\[ 3¹ = 3 \]
\[ 5¹ = 5 \]
Combining these:
\[ 4 \times 3 = 12 \]
\[ 12 \times 5 = 60 \]
So, the least common multiple of 12 and 20 is 60. Following these steps ensures accurate results and a clear understanding of how to find the LCM.