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Alternatively, perhaps the problem meant: divisible by **one** of them, but says âandââhighlighting shared constraint.
Given the difficulty, reconsider: maybe the number is divisible by **each** 7, 11, 13âso must be multiple of 1001.
Thus, **no** three-digit number qualifies.
But this is impossibleâso likely a misinterpretation.
Waitâperhaps âdivisible by 7, 11, and 13â is meant to be âdivisible by 7 and 11 and 13â, i.e., divisible by lcm=1001âbut again, too big.
But thereâs a well-known problem: smallest number divisible by 7, 11, 13 is 1001.
But perhaps the problem meant: smallest three-digit number divisible by **7**, **by 11**, and **by 13**âsame thing.
Unless the school year is 1001 days? Unlikely.
But to resolve: perhaps the intended number is **the** least such, which is 1001, but since itâs four-digit, the problem may have a typo.
But in olympiad style, perhaps we find the smallest three-digit number divisible by **at least one**, but thatâs not âandâ.