Multiply both sides of an equation by an expression?

Questions
1

For example, a ==b —> a * c == b * c.
Thanks.

2

In version 11.3 we have MultiplySides:

MultiplySides[x/3 == 7, 3]

In earlier version you can Map the multiplication:

Map[3 # &, x/3 == 7]
3

MultiplySides[a == b, c]

$\begin{array}{cc}
{ &
\begin{array}{cc}
a c=b c & c\neq 0 \
a=b & \text{True} \
\end{array}
\
\end{array}$

MultiplySides[a == b, c, GenerateConditions -> False]

a c=b c

4

function Map is what I am looking for.
Thanks.