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