Step 1: Determine the prime factorization requirements of a
If integer a is divisible by 3 and 14:

\(14=2 \times 7\) , so a must be divisible by 2 and 7.
Since a is also divisible by 3, a must be a multiple of \( \operatorname{LCM}(3,14)=42\) .
Therefore, a=42 k for some integer \(k \in\{\ldots,-2,-1,0,1,2, \ldots\}\) .


Step 2: Evaluate each statement

\( \quad a\) is divisible by 6 :

Since \( 6=2 \times 3\) and a is a multiple of \(42(42=6 \times 7\)), a is always divisible by 6 . (MUST BE TRUE)
$\quad a$ is equal to 42:
a could be 84,-42 , or 0 . It does not have to equal 42. (NOT NECESSARILY TRUE)
\(\quad a \) is divisible by 21:

Since \(21=3 \times 7\) and $a$ is a multiple of $42(42=21 \times 2), a$ is always divisible by 21 . (MUST BE TRUE)
\(\quad a\) is positive:

a could be negative (e.g., -42) or zero (0). (NOT NECESSARILY TRUE)


Correct Choices:

\( [\mathrm{x}] a\) is divisible by 6
\([\mathrm{x}] a\) is divisible by 21