Question ( Chrono Trigger )

I have one question, which is probably obvious but Im still curious. At the beginning of the game, when Marle gets sent into another time zone when she enters Luccas invention. Now, it was the pendant that got her in right ?
Well, chrono goes after her, with the pendant, Lucca says she will follow, but Chrono had the pendant with him, so how does she get through ?

Lucca invented the little wand looking thing that lets her jump through the portals.

i believe its called a gate key

Yeah, it's been a while since I've played.

How does she make the Gate Key again ?
I should replay CT some time....

Using the machine's system, she made a Pendant-Emulator, that we know as the Gate Key