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There are two common methods to find the Least Common Multiple (LCM) of two or more numbers:


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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

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