# What is the least common multiple of 2, 3, and 7?

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Apr 13, 2016

Least Common Multiple is $42$.

#### Explanation:

Multiples of $2$ are $\left\{2 , 4 , 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 , 24 , 26 , 28 , 30 , 32 , 34 , 36 , 38 , 40 , 42 , 44 , 46 , 48 , 50 , \ldots\right\}$

Multiples of $3$ are $\left\{3 , 6 , 9 , 12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 , 42 , 45 , 48 , 51 , . .\right\}$

Multiples of $7$ are $\left\{7 , 14 , 21 , 28 , 35 , 42 , 49 , 56 , \ldots\right\}$

Common multiples are $\left\{42 , \ldots\right\}$

Least Common Multiple is $42$.

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