Ononot — For which of the following linear Diophantine equations do i

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GCD & LCMhard

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For which of the following linear Diophantine equations do integer solutions exist? (Recall: $ax + by = c$ has integer solutions iff $\gcd(a,b) \mid c$ .)

I. $6x + 10y = 12$ II. $6x + 10y = 15$ III. $15x + 25y = 20$ IV. $15x + 25y = 100$