# How to find LCM of two numbers?

#### Understand the Problem

The question is asking how to calculate the least common multiple (LCM) of two numbers, which involves identifying a number that is a multiple of both given numbers. This can be done using methods such as prime factorization or the relationship between LCM and GCD (greatest common divisor).

Multiply the numbers together and divide by their GCD

To find the LCM of two numbers, multiply the numbers together and divide by their GCD.

#### Steps to Solve

1. Identify the two numbers you want to find the LCM for

Let's say the two numbers are $a$ and $b$.

2. Find the prime factors of both numbers

Break down both $a$ and $b$ into their prime factors.

3. Determine the highest power of each prime factor

For each prime factor that appears in the factorizations of $a$ and $b$, take the highest power found in any of the factorizations.

4. Multiply these highest powers together

The result will give you the least common multiple of $a$ and $b$.

Alternatively, you can use the relationship between the LCM and the GCD:

$$\text{LCM}(a, b) = \frac{a \times b}{\text{GCD}(a, b)}$$

To find the LCM of two numbers, multiply the numbers together and divide by their GCD.

The LCM is useful in problems involving adding, subtracting, or comparing fractions with different denominators.

#### Tips

A common mistake is neglecting to include all the highest powers of the prime factors when using the prime factorization method.

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