What two-digit positive integer is three less than a multiple of 7, and also three less than a multiple of 11?** But not.

February 22, 2026

What two-digit positive integer is three less than a multiple of 7, and also three less than a multiple of 11?** But not.

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But for olympiad creativity, perhaps the intended setup was:
Find a two-digit number such that it is **three less than a multiple of 7**, **three less than a multiple of 8**, and **three less than a multiple of 9** — same as before.
Alternatively, maybe the question meant:
Perhaps the number is such that $ x \equiv -3 \pmod{7} $, $ x \equiv -3 \pmod{8} $, $ x \equiv -3 \pmod{9} $, same.
But let’s suppose the intended LCM was smaller. Suppose the question meant:
"Three less than a multiple of 5, 6, and 7" — then $ \text{lcm}(5,6,7) = \text{lcm}(5,2\cdot3,7) = 210 $ — still too big.

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