How would you find the least common multiple of a bunch of numbers with each one starting at a different offset? I read about Euclid's algorithm and Bézout's identity but I'm too dumb to extrapolate it all to more than 2 numbers.

For example, how would you find the smallest number that satisfies each of these formulas without brute forcing it?

5434 + 8683*x
7258 + 7277*y
760 + 779*z