Hello, jethrotulL!

Even if you don't know (or understand) the Euclidean algorithm,

. . you can still solve it.

Solve by the Euclidean algorithm: .

We have: .

Solve for .[1]

Since is an integer, must be a multiple of 9.

. . That is: .

Solve for .[2]

Since is an integer, must be a multiple of 7.

. . The first time this happens is

Substitute into [2]: .

Substitute into [1]: .