Find the HCF and LCM of 9, 6, and 8. Divide the LCM of 160, 18, 21

For $9p^2q^3r^2$: $3^2 \cdot p^2 \cdot q^3 \cdot r^2$
For $6p^3q^2r^4$: $2^1 \cdot 3^1 \cdot p^3 \cdot q^2 \cdot r^4$
For $8p^2q^4r^3$: $2^3 \cdot p^2 \cdot q^4 \cdot r^3$

The HCF is found by taking the lowest power of each common prime factor (numerical and variable) present in all expressions.

• Numerical coefficients (9, 6, 8): There are no common prime factors other than 1. So, the HCF of the numerical coefficients is 1.
• Variable $p$: The lowest power is $p^2$.
• Variable $q$: The lowest power is $q^2$.
• Variable $r$: The lowest power is $r^2$.

The LCM is found by taking the highest power of each prime factor (numerical and variable) present in any of the expressions.

• Numerical coefficients (9, 6, 8): $9 = 3^2$ $6 = 2 \times 3$ $8 = 2^3$ The highest power of 2 is $2^3$. The highest power of 3 is $3^2$. LCM of (9, 6, 8) $= 2^3 \times 3^2 = 8 \times 9 = 72$.
• Variable $p$: The highest power is $p^3$.
• Variable $q$: The highest power is $q^4$.
• Variable $r$: The highest power is $r^4$.

The HCF is $\boxed{p^2q^2r^2}$ and the LCM is $\boxed{72p^3q^4r^4}$.

: Find the LCM of $160, 180, 240$.
(The question asks to "Divide the LCM", but does not specify by what. We will find the LCM.)

• Highest power of 2: $2^5$ (from 160)
• Highest power of 3: $3^2$ (from 180)
• Highest power of 5: $5^1$ (from 160, 180, 240)

The LCM of $160, 180,$ and 240 is $\boxed{1440}$.