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2nd Road Race, National Road Championships - Simpleprint

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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$11$.
Others: 4 = $2^2$, 6 = $2\cdot3$, 10 = $2\cdot5$, 12 = $2^2\cdot3$. So...
\mathrm{lcm} = 2^3 \cdot 3^2 \cdot 5 \cdot 7 \cdot 11 = 8 \cdot 9 \cdo...
$8 \cdot 9 = 72$,
$72 \cdot 5 = 360$,
$360 \cdot 7 = 2520$,
$2520 \cdot 11 = 27720$.
So $\mathrm{lcm} = 27720$.
Now find smallest $k$ such that $27720k > 1,\!000,\!000$:
k > \frac{1,\!000,\!000}{27720} \approx 36.06.

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\[ 14x = 43 \]
\[ x = rac{43}{14} \]
Substitute \(x\) back into the first equation:
\[ 2\left(rac{43}{14}
ight) + 3y = 16 \]
\[ rac{86}{14} + 3y = 16 \]
\[ 3y = 16 - rac{43}{7} \]
\[ 3y = rac{112}{7} - rac{43}{7} \]
\[ 3y = rac{69}{7} \]
\[ y = rac{69}{21} = rac{23}{7} \]

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