The largest four-digit number which when divided by 10, 11 and 8 leaves remainder 7 in each case is:
9687
The required number is of the form \(\text{LCM}(10, 11, 8) \times k + 7\) for some integer \(k\).
\(\text{LCM}(10, 11, 8) = 440\).
The largest four-digit multiple of 440 is \(440 \times 22 = 9680\) (since \(440 \times 23 = 10120\) exceeds four digits).
Adding the remainder: \(9680 + 7 = 9687\).
Hence, the largest four-digit number satisfying the condition is 9687.
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