Consecutive integers

Let \(a < b < c < d\) be four consecutive positive integers such that

  • \(a\) is divisible by 5,
  • \(b\) is divisible by 7,
  • \(c\) is divisible by 9, and
  • \(d\) is divisible by 11.

Find the minimum value of \(a+b+c+d.\)

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