Understanding Least Common Multiple (LCM)

Key Concepts

• T.L.A.: Three Letter Acronym, typically in reference to mathematical terms like L.C.M. and G.C.F.
• Least Common Multiple (LCM): The smallest multiple shared by two or more numbers.

Comparison with GCF

• Greatest Common Factor (GCF): Largest factor common to two or more numbers.
• Both LCM and GCF use the term "common" but approach numbers differently; one focuses on factors, the other on multiples.

Finding LCM

1. Basic Method:

   • List multiples of each number by multiplication.
   • Identify the smallest common multiple from the lists.
   • Example with numbers:
     • Multiples of 3: 3, 6, 9, 12, 15, ...
     • Multiples of 4: 4, 8, 12, 16, ...
     • Least Common Multiple of 3 and 4: 12.

2. Step-by-Step Process for Larger Numbers:

   • Example: Finding LCM for 12 and 14.
   • List multiples sequentially until a common one is found.
   • Multiples of 12: 12, 24, 36, 48, ...
   • Multiples of 14: 14, 28, 42, 56, ...

Drawbacks of Listing Method

• Unknown Quantity: You don’t know how many multiples to list initially to find the LCM.
• Labor-Intensive: Can be cumbersome for larger numbers.

Alternative Approach

• Prime Factorization Method: Mentioned as a more efficient approach, to be covered in the next video.

Conclusion

Finding the LCM by listing multiples is straightforward but may be inefficient, particularly with larger numbers. The video hints at more advanced techniques for efficiency — an introduction to simplifying the process is expected to be covered later.