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58, 118, 178, ...

That is all numbers that are 60n - 2 where n = 1, 2, 3, ...

It has a remainder of 3 when divided by 5, means the last digit must be 3 or 8.

It also has a remainder of 2 when divided by 4, means that the number must be even, so the last digit must be 8.

It also has a remainder of 1 when divided by 3, means it must be 1 more than a multiple of 3 that ends in 7. So it must be 28, 58, 88, 118, ..., (each number 30 more than the last) but 28, 88, ... are divisible by 4, so only 58, 118, ... (each number 60 more than the last) need be considered.

It also has a remainder of 4 when divided by 6, means it must be 4 more than a multiple of 6 that ends in 4. So it must be 58, 118, ...

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