Finding the Least Common Multiple (LCM): Step-by-Step Guide and Importance in Mathematics

least common multiple (LCM)

The least common multiple (LCM) is a concept in mathematics that is used to find the smallest multiple that two or more numbers have in common

The least common multiple (LCM) is a concept in mathematics that is used to find the smallest multiple that two or more numbers have in common.

To find the LCM of two numbers, you can follow these steps:

Step 1: Start by writing down the prime factorization of each number.
For example, let’s find the LCM of 12 and 18.
The prime factorization of 12 is 2^2 * 3^1 (2 squared times 3 once).
The prime factorization of 18 is 2^1 * 3^2 (2 once times 3 squared).

Step 2: Identify the highest power of each prime factor that appears in either number.
In this case, the highest power of 2 is 2^2 (from 12) and the highest power of 3 is 3^2 (from 18).

Step 3: Multiply all the highest powers of the prime factors together.
In this case, the LCM of 12 and 18 is 2^2 * 3^2, which equals 4 * 9 = 36.

So, the LCM of 12 and 18 is 36.

When dealing with more than two numbers, you can find the LCM by following the same steps. For example, let’s find the LCM of 12, 18, and 24.

The prime factorization of 12 is 2^2 * 3^1.
The prime factorization of 18 is 2^1 * 3^2.
The prime factorization of 24 is 2^3 * 3^1.

Identifying the highest powers, we get 2^3 * 3^2, which equals 8 * 9 = 72.

So, the LCM of 12, 18, and 24 is 72.

The LCM is a useful concept in many areas of mathematics, such as fractions, ratios, and solving equations. It allows us to find a common multiple that can be used to simplify calculations and solve problems more easily.

More Answers: