How to Work Out the Lowest Common Multiple?

To work out the Lowest Common Multiple (LCM) of two or more numbers, you need to find the smallest number that is a multiple of all the given numbers. Here's a step-by-step guide:

1. List the Multiples:

• For each number, list out its first several multiples. A multiple is simply the number multiplied by an integer (e.g., the multiples of 3 are 3, 6, 9, 12, 15, and so on).

2. Identify Common Multiples:

• Look for multiples that are common to all of the lists you created.

3. Find the Smallest Common Multiple:

• From the common multiples you've identified, find the smallest one.

4. The LCM:

• This smallest common multiple is the LCM of the original numbers.

Example:

Let's find the LCM of 4 and 6.

Step 1: List Multiples

• Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36,...
• Multiples of 6: 6, 12, 18, 24, 30, 36, 42,...

Step 2: Identify Common Multiples

• Common multiples of 4 and 6: 12, 24, 36,...

Step 3: Find the Smallest Common Multiple

• The smallest common multiple is 12.

Step 4: The LCM

• Therefore, the LCM of 4 and 6 is 12.

Alternative Method: Prime Factorization

Another method for finding the LCM, especially useful for larger numbers, involves prime factorization:

1. Find the Prime Factorization: Determine the prime factorization of each number.
2. Identify Highest Powers: For each prime factor that appears in any of the factorizations, identify the highest power to which it is raised.
3. Multiply the Highest Powers: Multiply together all of these highest powers. The result is the LCM.

Example (Prime Factorization Method):

Let's find the LCM of 12 and 18.

1. Prime Factorization:

   • 12 = 2² x 3
   • 18 = 2 x 3²

2. Identify Highest Powers:

   • Highest power of 2: 2²
   • Highest power of 3: 3²

3. Multiply the Highest Powers:

   • LCM = 2² x 3² = 4 x 9 = 36

Therefore, the LCM of 12 and 18 is 36.