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You can solve this using algebra. The hardest part, as usual, is setting up the problem. Here's how I would do it.
First let's choose a representation for the lowest integer. We could just say it equals x, but that wouldn't incorporate our knowledge that it's even. So I think we should represent it as 2x. Then, since consecutive integers are two apart, we can represent the other three by 2x + 2, 2x + 4, and 2x + 6.
Now all we have to do is solve
2x + (2x + 2) + (2x + 4) + (2x + 6) = 60
Combine like terms and we get
8x + 12 = 60
which gives
8x = 48
and finally
x = 6
So the lowest number is 2x = 12, and the rest are 14, 16, and 18.
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