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Problem #5 · August 1, 2026

Greatest common divisor EKUB and least common multiple EKUK

When 250 and 172 are divided by a certain natural number, the remainders are 10 and 4, respectively. Find the largest such number.
  1. A2
  2. B4
  3. C24
  4. D48
  5. E168

WORKED EXAMPLE

Solution

If dividing 250 leaves a remainder of 10, then 250−10=240250 - 10 = 240 is divisible by the required number without a remainder; similarly, 172−4=168172 - 4 = 168 is also divisible by it. The largest such number is EKUB(240;168)EKUB(240; 168): 240=24⋅3⋅5240 = 2^4 \cdot 3 \cdot 5, 168=23⋅3⋅7168 = 2^3 \cdot 3 \cdot 7, EKUB =23⋅3=24= 2^3 \cdot 3 = 24. Since 24>1024 > 10, the remainder condition is also satisfied.
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