# What is the least common multiple for 4 and 6 ?

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Feb 12, 2017

$12$

#### Explanation:

To find the LCM of two numbers (or any amount of numbers) we must first find the prime factorization of each number separately.

Let's take the number $4$:

$4 = 2 \cdot 2$

$4 = {2}^{2}$

Now the number $6$:

$6 = 2 \cdot 3$

From here we must determine the factors of each number with the highest exponent.

For example, both the number $4$ and the number $6$ share the factor $2$. But $2$ appears twice in the prime factorization of $4$. So we must use that. We now have:

${2}^{2}$

Another factor that appears is the number $3$. $3$ only appears in the prime factorization of $6$, so we must use that. Now we have:

${2}^{2} \cdot 3$

Simplify from here.

$4 \cdot 3$

$12$

So therefore, the LCM of $4$ and $6$ is $12$.

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