Paste() - Get all possible combinations from multiple vectors

Hello fellow R-users,

Given are three vectors and the outcome would be all possible combinations in combination with the paste() function.
For example:

x <- c(1:3)
y <- letters[1:3]
z <- LETTERS[1:3]

My result would thus be 18 names based on all possible combinations between these vectors:
"1 a A" "1 a B", "1 a C", "1 b A", "1 b B", "1 b C", "1 c A", "1 c B", "1 c C", etc.

To solve the issue above I would use:

paste(rep(x, each=9), rep(y, each=6), z)

This is a very straightforward example, but when I have vectors of different sizes, it will be much more difficult (for me) to create this. Is there an easier way to do this?

Many thanks in advance,

?-- Stan

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