What is the LCM and GCD OF 3^13*5^17,2^12*7^21 (WITH SOLUTION)?

 3^13*5^17,2^12*7^21 Least Common Multiple (LCM) ?

$$\small{\begin{array}{l|rclclclcl}\text{Number 1:} & 3^{13}*5^{17} &=& 2^0 &*& 3^{\textcolor[rgb]{1,0,0}{13}} &*& 5^{\textcolor[rgb]{1,0,0}{17}} &*& 7^0 \\\text{Number 2:} & 2^{12}*7^{21} &=& 2^{\textcolor[rgb]{1,0,0}{12}}&*& 3^0 &*& 5^0 &*& 7^{\textcolor[rgb]{1,0,0}{21}}\\ \hline \text{The greatest Exponent}\\ \text{ of each prime number} &\text{LCM}&=& 2^{\textcolor[rgb]{1,0,0}{12}}&*&3^{\textcolor[rgb]{1,0,0}{13}} &*&5^{\textcolor[rgb]{1,0,0}{17}} &*& 7^{\textcolor[rgb]{1,0,0}{21}}\end{array}}}$$

3^13*5^17,2^12*7^21 Greatest Common Devisor(GCD) ?

$$\small{\begin{array}{l|rclclclcl}\text{Number 1:} & 3^{13}*5^{17} &=& 2^{\textcolor[rgb]{1,0,0}{0}} &*& 3^{13} &*& 5^{17} &*& 7^{\textcolor[rgb]{1,0,0}{0}} \\\text{Number 2:} & 2^{12}*7^{21} &=& 2^{12}&*& 3^{\textcolor[rgb]{1,0,0}{0}} &*& 5^{\textcolor[rgb]{1,0,0}{0}} &*& 7^{21}\\
\hline \text{The lowest Exponent}\\ \text{ of each prime number} &\text{GCD}&=& 2^{\textcolor[rgb]{1,0,0}{0}}&*&3^{\textcolor[rgb]{1,0,0}{0}} &*&5^{\textcolor[rgb]{1,0,0}{0}} &*& 7^{\textcolor[rgb]{1,0,0}{0}} = 1*1*1*1=1
\end{array}}}$$