1. Let's clarify the concept of LCM (Least Common Multiple). The LCM of two or more numbers is the smallest number that is a multiple of all the given numbers. 2. The formula to find the LCM using prime factorization is: $$\text{LCM} = \prod \text{(highest powers of all prime factors)}$$ 3. Important rules: - The LCM is always greater than or equal to the greatest number in the set. - If one number divides another, the LCM is the larger number. 4. Example: Find the LCM of 12 and 18. - Prime factors of 12: $2^2 \times 3$ - Prime factors of 18: $2 \times 3^2$ - Take highest powers: $2^2$ and $3^2$ - Multiply: $2^2 \times 3^2 = 4 \times 9 = 36$ 5. So, the LCM of 12 and 18 is 36. This method ensures you find the smallest number divisible by both numbers without confusion.