If d = gcd(a, m) and d|c, then show that the congruence ax ≡ c (mod m) is equivalent to a x≡c (modm).

If $d = gcd(a, m)$ and $d|c$, then show that the congruence $ax equiv c$ (mod $m$) is equivalent to

$frac{a}{d}$ $x equiv frac{c}{d}$ $($mod $frac{m}{d}).$