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Problem #23 · August 19, 2026

Common fractions

For the fraction n18\frac{n}{18} to be in lowest terms, which of the following values can nn take?
  1. A6
  2. B12
  3. C9
  4. D15
  5. E25

WORKED EXAMPLE

Solution

Since 18=2⋅3218=2\cdot3^2, for the fraction to be in lowest terms, nn must be divisible by neither 2 nor 3. The number 25=5225=5^2 has neither of these divisors, so EKUB(25,18)=1(25,18)=1. Each of the other choices is divisible by 2 or 3, so the fraction can be reduced.
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