this might get best visibility in Norns: clock, but i’m running 32nd-syncing clocks in cheat codes without any trouble. clock.sync(1) is always a 1/4 note, so clock.sync(1/8) should get you stable 32nd 
i like having separate clocks for different components, especially because it makes management + debugging easy.
where you’d want a lowest common denominator is if you want different steps to have different note length values – this gets into step sequencer territory, which might not be relevant to your goals, but it’s something that tripped me up at first because I thought that changing the clock.sync() argument would magically let me sequence.
programmatically changing the clock.sync() value is not the same as saying “gimme a quarter note and then an eighth note and then a whole note and then a…” – it’s just saying that “when the next clock tick of x value happens, then do y”.
so if you clock.sync(1/4) and then immediately clock.sync(1/2), it won’t be the same as a 16th note followed by an eighth note, because you’ll have to wait a 16th note until the next eighth note clock value occurs. does that explanation make sense? it’s wibbly and just based on hours of being like “the heck is happening?”, so happy to put better words into it.
instead, I’ve had success using a “runner” that has an awareness of a given step’s duration at the lowest common denominator, driven by a clock at the lowest common denominator. so, if i want to have a 1/4 note step followed by an 1/8th note step followed by a 1/32nd note, i’d do something like this:
function advance(target)
while true do
clock.sync(1/8)
if runner == 1 then
play_note_or_whatever()
end
if runner == step_duration[step] then
step = step + 1
runner = 0
end
if step > seq_end_point then
step = seq_start_point
end
runner = runner + 1
end
end
end
where step_duration is a table of durations (defined by how many ticks it takes to count a step value at the desired resolution). so, a 1/4 note step in a sequencer that goes down to 32nd notes would mean 8 ticks, because 8/32 = 1/4.
hope that helps?