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CAT 2022 Slot 1 · Quant · Remainders and Divisibility · medium

Find the largest 3-digit number that is divisible by both 7 and 11.

Numerical answer

Find the largest 3-digit number that is divisible by both 7 and 11.
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Answer: 924

A number divisible by both 7 and 11 must be divisible by their LCM = 77 (since 7 and 11 are co-prime). The largest 3-digit multiple of 77 is found by dividing 999 by 77: 999 ÷ 77 ≈ 12.97, so the largest integer multiple is 77 × 12 = 924.
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