Question

Se a | c e b | d então ab | cd.

Answer 1

$\large\boxed{\begin{array}{l}\rm\bigg |^a_c\iff c=a\cdot q_1\\\\\rm \bigg|^b_d\iff d=b\cdot q_2\\\rm multiplicando\,as\,igualdades\,anteriores\,temos\\\rm c\cdot d=a\cdot b\cdot q_1\cdot q_2\\\rm fazendo~q_1\cdot q_2=q,q\in\mathbb{Z}~temos\\\rm c\cdot d=a\cdot b\cdot q\\\rm c\cdot d=(a\cdot b)\cdot q\\\rm mas~se~c\cdot d= (a\cdot b)\cdot q~~\underrightarrow{\rm de~\!\!f}~\bigg|^{ab}_{cd}\end{array}}$