What is the **least common multiple** (LCM) of $30$ and $75$?

Prime-factor each: $30 = 2 \times 3 \times 5$ and $75 = 3 \times 5^2$. The LCM takes the highest power of every prime that appears in either: $2^1 \times 3^1 \times 5^2 = 2 \times 3 \times 25 = 150$. - Option A ($15$) is the **GCD**, not the LCM — a classic swap. - Option B ($75$) is a multiple of 75 but $75 / 30$ is not an integer, so 75 is not a multiple of 30. - Option D ($2{,}250 = 30 \times 75$) is the product; product equals LCM only when GCD $= 1$.