Divisibility proof: if a divides b and c, must one of b or c divide the other?

[dgamma3]

is this true or false:

If a|b and a|c, then one (or both) of b|c or c|b holds.

if I want to disprove this, can I:

let a = 5, x = 2 and y = 3.

b=ax
c=ay

then c=bz
and c = bg doesn't hold.

 

[Bacle2]

Why make it so complicated? You constructed a counter-example:

a=5 , b=10 c=15 , and neither 10|15 nor 15|10.