# What is the least common multiple (LCM) of 2 and 6?

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1
Mar 4, 2018

$6$

#### Explanation:

You can quickly think about the problem by using knowledge of how $6$ is a multiple of $2$, and that it is also the second number itself. With this knowledge, you can infer that it is the LCM of the numbers.

However, if you aren't sure, you can always list the multiples of both numbers:

$2 : 2 , 4 , 6$

$6 : 6$

$6$ is the first multiple found in both numbers, so it is the LCM.

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Russell Share
Mar 4, 2018

The LCM would be 6 for the values of 2 and 6.

#### Explanation:

The LCM would be calculated by finding the prime factorization of both numbers, then taking the product of the sets of primes with the highest exponent value among them.
In this case, the values are 2 and 6.

Prime factorization of 2 = 2 x 1 = ${2}^{1} \cdot {1}^{1}$
Prime factorization of 6 = 3 x 2 = ${2}^{1} \cdot {3}^{1} \cdot {1}^{1}$
Using the set of prime numbers from each set with the highest exponent value we take ${2}^{1} \cdot {3}^{1} \cdot {1}^{1}$
Therefore LCM(2, 6) = 6

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