What is the least common multiple of the first ten positive integers?
\(2,3,\dots, 10 = \{2^1, 3^1, 2^2, 5^1, 2^1 \cdot 3^1,7^1, 2^3, 3^2, 2^1\cdot 5^1\}\\ \text{Using the max exponents for common factors we obtain}\\ LCM = 2^3 \cdot 3^2 \cdot 5^1 \cdot 7^1 = 2520\)
