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Q. $P$ is the LCM of $2,4,6,8,10, Q$ is the LCM of 1,3 , $5,7,9$, and $L$ is the LCM of $P$ and $Q$. Then, which of the following is true?

Number System

Solution:

$P$ is the $LCM$ of $2,4,6,8,10$.
$\therefore P=3(8)(5)$
$Q$ is the LCM of $1,3,5,7,9$.
$\therefore Q=5(7)(9)$
$L$ is the LCM of $P, Q$
$\therefore L=3(8)(5) 21 \text { or } 5(7)(9) 8 \text {, i.e., } 21 P \text { or } 8 Q \text {. }$