Waitâperhaps the problem says âdivisible by 7, 11, and 13â but allows smaller multiples? Noâ1001 is the smallest.

February 22, 2026

Waitâperhaps the problem says âdivisible by 7, 11, and 13â but allows smaller multiples? Noâ1001 is the smallest.

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Waitâperhaps the number is divisible by **each** of 7, 11, and 13âmeaning divisible by their **product**, so $ z $ must be a multiple of 1001. The smallest such $ z $ is 1001, but it is not three-digit.
Therefore, **no** three-digit number satisfies this.
But this cannot beâlikely an error in assumption.
Unless the number is not required to be divisible by the product, but by **some**âbut no.
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.

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