The Least Common Multiple (LCM) of two or more numbers is the smallest number that is a multiple of each of the numbers. To calculate the LCM, there are several methods you can use. Here are three common methods:

1. Prime Factorization Method:

• Step 1: Find the prime factorization of each number.
• Step 2: For each prime factor, take the highest power of that factor from the factorizations.
• Step 3: Multiply these highest powers together to get the LCM.

Example: Find the LCM of 12 and 18.

• Prime factors of 12: $2^2 \times 3^1$
• Prime factors of 18: $2^1 \times 3^2$
• LCM = $2^2 \times 3^2 = 4 \times 9 = 36$

2. Division Method (also called Ladder Method):

• Step 1: List the numbers side by side.
• Step 2: Divide by a common prime factor (if it exists for all numbers) and write the results below.
• Step 3: Continue dividing by common prime factors until no more common factors remain.
• Step 4: Multiply all the divisors and the final numbers to get the LCM.

Example: Find the LCM of 12 and 18.

2 & 12 & 18 \\ 2 & 6 & 9 \\ 3 & 3 & 9 \\ & 1 & 3 \\ & 1 & 1 \\ \end{array}$$ Multiply the divisors: $$2 \times 2 \times 3 \times 3 = 36$$ ### 3. **Using the Relationship Between LCM and GCD**: The formula for the LCM of two numbers $$a$$ and $$b$$ is: $$\text{LCM}(a, b) = \frac{a \times b}{\text{GCD}(a, b)}$$ where GCD is the greatest common divisor of the numbers. **Example**: Find the LCM of 12 and 18. - GCD(12, 18) = 6 - LCM = $$\frac{12 \times 18}{6} = 36$$ Each method gives you the same result. Choose the one that works best for the situation. Do you want more details on any of the methods or have any questions? ### 5 Related Questions: 1. What is the difference between LCM and GCD? 2. How do you calculate the GCD of two numbers? 3. Can LCM be used in solving word problems involving multiple quantities? 4. How do you calculate LCM for more than two numbers? 5. What are the applications of LCM in real life? **Tip**: When dealing with larger numbers, using the GCD method to find the LCM can be quicker than prime factorization.