Test if a list is a constant integer multiple of another list

Same principle as kglr's, but using a much cheaper test:

DeleteDuplicates[{{1, 1, 1}, {1, 1, 2}, {2, 2, 2}, {2, 2, 4}, {3, 3, 5}},
                 Norm[Cross[##]] == 0 &]
   {{1, 1, 1}, {1, 1, 2}, {3, 3, 5}}

---

For eliminating only integer multiples:

DeleteDuplicates[{{2, 2, 2}, {2, 2, 4}, {3, 3, 5}, {3, 3, 6}, {5, 5, 5}, {8, 8, 8}}, 
                 Norm[Cross[##]] == 0 &&
                 (And @@ Thread[Divisible[##] || Divisible[#2, #1]]) &]
   {{2, 2, 2}, {2, 2, 4}, {3, 3, 5}, {3, 3, 6}, {5, 5, 5}}

Update:

I want to eliminate all the lists that are constant integer multiples of another list.

As noted by Simon in a comment all the methods in my original answer eliminate rows that are rational multiples of another row.

To eliminate a row when it is an integer multiple of another row, we can use

ClearAll[f]
f = DeleteDuplicates[#, Reduce[# == k #2 || m # == #2, {k, m}, Integers] =!= False &]

or

f = DeleteDuplicates[#, Resolve[Exists[{k, m}, # == k #2 || m # == #2], Integers] &] &

Examples:

f @ ex1

{{1, 1, 1}, {1, 1, 2}, {3, 3, 5}}

ex2 = {{1, 1, 2}, {2, 2, 2}, {2, 2, 4}, {3, 3, 5}, {5, 5, 5}};
f @ ex2 

{{1, 1, 2}, {2, 2, 2}, {3, 3, 5}, {5, 5, 5}}

which is the correct result. The other methods posted so far all eliminate {5, 5, 5} in ex2 because it is a rational multiple of {2, 2, 2}:

DeleteDuplicates[ex2, MatrixRank@{##} == 1 &]

{{1, 1, 2}, {2, 2, 2}, {3, 3, 5}}

jm @ ex2 == gb @ ex2 == DeleteDuplicates[ex2, MatrixRank@{##} == 1 &]

True

Original answer:

DeleteDuplicates[ex1, MatrixRank @ {##} == 1 &]
DeleteDuplicates[ex1, Length @ SingularValueList @ {##} == 1 &]
DeleteDuplicates[ex1, RowReduce[{##}][[2]] == {0, 0, 0} &]

{{1, 1, 1}, {1, 1, 2}, {3, 3, 5}}

GatherBy is much faster than the pairwise-compare of DeleteDuplicates with a custom comparator.

jm = DeleteDuplicates[#, Norm[Cross[##]] == 0 &] &;

gb = GatherBy[#, #/Max[1, GCD @@ #] &][[All, 1]] &;

Needs["GeneralUtilities`"]

BenchmarkPlot[{jm, gb}, RandomInteger[9, {#, 3}] &, 5, "IncludeFits" -> True]

Other examples:

• Checking for duplicates in sublists