In this article, we will break down how to calculate the **LCM of 18, 24, and 42** using simple and effective methods. The **Least Common Multiple (LCM)** is the smallest number that is a multiple of two or more numbers. Let’s dive into the steps to find the LCM of these numbers!

## Steps to Find the LCM of 18, 24, and 42

We’ll use the **prime factorization method** to calculate the LCM, which is one of the most efficient ways to find it.

#### Step 1: Prime Factorization of Each Number

First, we need to find the prime factors of each number.

**Prime factorization of 18:**

18 = 2×3×3 = 2×3^{2}**Prime factorization of 24:**

24 = 2 × 2 × 2 × 3 = 2^{3}× 3**Prime factorization of 42:**

42 = 2 × 3 × 7 = 2 × 3 × 7

#### Step 2: Identify the Highest Powers of Prime Factors

To find the LCM, we take the highest power of each prime number that appears in the prime factorizations.

- The prime factors are 2, 3, and 7.
- The highest power of
**2**is ( 2^{3}) (from 24). - The highest power of
**3**is ( 3^{2}) (from 18). - The highest power of
**7**is ( 7 ) (from 42).

#### Step 3: Multiply the Highest Powers Together

Now, we multiply these together to find the LCM:

LCM = 2^{3} × 3^{2} × 7 = 8 × 9 × 7

LCM = 72 × 7 = 504

So, the **LCM of 18, 24, and 42** is **504**.

### Verification of the LCM

To confirm, let’s list the multiples of 18, 24, and 42 and check if 504 is indeed the smallest common multiple.

- Multiples of 18: 18, 36, 54, 72, …,
**504** - Multiples of 24: 24, 48, 72, 96, …,
**504** - Multiples of 42: 42, 84, 126, 168, …,
**504**

Since 504 is the first common multiple in all three lists, the LCM is correct.

### Conclusion

The **LCM of 18, 24, and 42** is **504**. This method of using prime factorization ensures accuracy and efficiency when finding the Least Common Multiple of multiple numbers. Whether you’re solving math problems or handling real-life applications like scheduling or managing frequencies, knowing how to calculate the **LCM** can be incredibly useful.

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