I'm setting up my first semi modular system.

One sequencer is the main clock! How can I multiply it so my other sequencer will run at double or treble the tempo but still be locked to the main sequencer?

Do I need a eurorack module to do this?

My set up -

Arturia Minibrute 2S
Elektron Analogue 4 Mk2
Make Noise O-Coast

EDP Wasp
Roland Juno 6 (pre midi)
Would you choose the Arturia or the Elektron as main clock?

I think what you want to find is a clock-divider module. It's the opposite of a clock multiplier, but much more common and usually cheaper. You'd run the 2x or 3x division into your sequencer, and then the 1x main clock into your faster sequencer. I love the clock-divider, it's the heart beat of my modular system, there are so many uses for one of these if you do anything with rhythm.

I have one of these, it doubles as both clock + divider, and has lots of switches to make it quite interactive.

There are ton of different options out there for this, so be sure to look around and see if some of the different versions fit your needs better. For example, if you already have a clock module, and want just a single channel divider/multiplier then you could get this one (which has a neat CV input):

But I still prefer the 4hp one I have because it is also my main clock, plus has 4 simultaneous outputs with 3 division modes and a reset.

My suggestion, even though it requires a bit of space, would be the 4ms Quad Clock Divider plus the QCD Expander. Lots of functionality...for pretty much anything you need to do math-wise with timing, it's perfect. Sort of a misnomer, also, as it does both division and multiplication of incoming pulses.

As for clock generation, in theory you can use BOTH as long as you keep the timing chains separate. Or, for more fun, you can use a Boolean logic module to set the timing gate pulses against each other at different rates and have the logic generate a totally new timing/rhythmic structure based on the logic state plus timing between clocks. EMW makes a very comprehensive logic module with lots of different gates, inverters, plus a pulse divider all in 14 hp. They actually have a pretty good (and inexpensive!) line of clock modifiers, including trig-to-gate converters that allow adjusting the clock pulse duty cycle, trig/gate delays for shifting pulse coincidence, etc.

Clocking doesn't get enough respect...there's actually loads of possibilities for creating elaborate rhythmic structures just by tinkering with basic timing. You could theoretically get just as busy working your timing modifiers as any other part, going nuts on creating cross- and polyrhythms.

The SDS Digital RIT_M can do multiply from the gate if a clock is tapped in first.
Like this:
Patch in the Clock, tap pad 4 times along with the beat and loop pad
Adjust PPQN up for 2x, 4x, 8x etc, or down for /2 /3 /4 etc
If the pad isn't quantized to the clock, the taps can have swing or missing clocks etc. which can be interesting!