7. There is a positive integer, its $\frac{1}{2}$ is the square of an integer, its $\frac{1}{3}$ is the cube of an integer, and its $\frac{1}{5}$ is the fifth power of an integer. Then the minimum value of this number is . $\qquad$
7. $2^{15} \times 3^{10} \times 5^{6} \quad$ Detailed explanation: Let's assume this number is $2^{a} \times 3^{b} \times 5^{c}$, then $a \equiv 1(\bmod 2), b \equiv 0(\bmod 2)$, $c \equiv 0(\bmod 2), a \equiv 0(\bmod 3), b \equiv 1(\bmod 3), c \equiv 0(\bmod 3), a \equiv 0(\bmod 5), b \equiv 0(\bmod 5), c \equiv 1(\bmod 5)$. $\therefore a=15, b=10, c=6, \therefore$ the minimum value is $2^{15} \times 3^{10} \times 5^{6}$.