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Home » Move Into Style: The Trailblazing Terrazzo Floor Trends Taking Over Homes! - High Altitude Science

Move Into Style: The Trailblazing Terrazzo Floor Trends Taking Over Homes! - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 \text{lcm}(12, 15) = 60

📌 So we are looking for the smallest three-digit number $x$ such that $x \equiv 1 \pmod{7}$ and $x \equiv 0 \pmod{60}$.

📌 Let $x = 60k$. Then we solve $60k \equiv 1 \pmod{7}$. Since $60 \equiv 4 \pmod{7}$, we solve:

📌 4k \equiv 1 \pmod{7}

📌 Multiplying both sides by the modular inverse of 4 modulo 7, which is 2 (since $4 \cdot 2 = 8 \equiv 1 \pmod{7}$), we get:

📌 k \equiv 2 \pmod{7}

📌 So $k = 7m + 2$. Then $x = 60k = 60(7m + 2) = 420m + 120$. We seek the smallest three-digit such $x$:

📌 x = 420m + 120 \geq 100 \Rightarrow m \geq 0

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We now find all $ \theta \in [0^\circ, 360^\circ] $ by plugging intege...
For $ \theta = 10^\circ + 120^\circ k $:
$ k = 0 $: $ 10^\circ $
$ k = 1 $: $ 130^\circ $
$ k = 2 $: $ 250^\circ $
$ k = 3 $: $ 370^\circ $ → too large
For $ \theta = 110^\circ + 120^\circ k $:
$ k = 0 $: $ 110^\circ $
$ k = 1 $: $ 230^\circ $
$ k = 2 $: $ 350^\circ $

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