1. Listing Multiples:

This method involves listing the multiples of each number until you find a number that appears on both lists.

Then, you check for the smallest common multiple.
Here's how it works:

Write down the two numbers you want to find the LCM of.

List the first few multiples of each number.

Compare the lists and find the first number that appears on both.

That number is the LCM, unless you find a smaller common multiple further down the lists.
2. Prime Factorization:

This method is more efficient for larger numbers.

It involves finding the prime factorization of each number and then multiplying the highest powers of each prime factor together.
Here's how it works:

Find the prime factorization of each number (break each number down to its prime components).

Identify the highest power of each prime factor that appears in any of the numbers.

Multiply all the prime factors together, using the highest exponent seen for each prime factor.
Example:
Let's find the LCM of 12 and 18 using both methods:

Listing Multiples:

Multiples of 12: 12, 24, 36, 48, ...

Multiples of 18: 18, 36, 54, ...

LCM = 36 (the smallest number common to both lists)

Prime Factorization:

Prime factorization of 12: 2 x 2 x 3

Prime factorization of 18: 2 x 3 x 3

LCM = 2 x 2 x 3 x 3 (highest powers of each prime factor) = 36
Both methods give you the same answer: LCM of 12 and 18 is 36.
Choose the method that best suits your needs and the complexity of the numbers you're working with