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Problem #85 · October 20, 2026

EKUB — greatest common divisor and EKUK — least common multiple

The greatest common divisor of two natural numbers equals 8, and their least common multiple equals 120. If one of the numbers is 24, find the other.
  1. A5
  2. B15
  3. C16
  4. D30
  5. E40

WORKED EXAMPLE

Solution

For two numbers, the identity a⋅b=EKUB⋅EKUKa \cdot b = EKUB \cdot EKUK holds. Therefore b=8⋅12024=96024=40b = \frac{8 \cdot 120}{24} = \frac{960}{24} = 40. Check: EKUB(24;40)=8EKUB(24; 40) = 8, EKUK(24;40)=120EKUK(24; 40) = 120 — the conditions are satisfied.
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