How to get LCM?

The Least Common Multiple (LCM) can be found through prime factorization. Here's how:

Finding the LCM Using Prime Factorization

1. Prime Factorization: Find the prime factorization of each number.
2. Identify Common and Uncommon Factors: List all prime factors that appear in any of the factorizations. For each prime factor, take the highest power that appears in any of the factorizations.
3. Multiply: Multiply all the prime factors (with their highest powers) together. The result is the LCM.

Example:

Let's find the LCM of 12 and 15.

1. Prime Factorization:

   • 12 = 2 x 2 x 3 = 2² x 3
   • 15 = 3 x 5

2. Identify Common and Uncommon Factors:

   • The prime factors are 2, 3, and 5.
   • The highest power of 2 is 2².
   • The highest power of 3 is 3¹.
   • The highest power of 5 is 5¹.

3. Multiply:

   • LCM (12, 15) = 2² x 3 x 5 = 4 x 3 x 5 = 60

Therefore, the LCM of 12 and 15 is 60.