# What is the LCM of 21m^2n, 84mn^3?

$L C M \left(21 {m}^{2} n , 84 m {n}^{3}\right) = 84 {m}^{2} {n}^{3}$
Numerical part: $84$ is an exaclt multiple of $21$ (namely, $21 \cdot 4$), so $L C M \left(21 , 84\right) = 84$.
Literal part: we must take all the variables which appear, and take them with the highest exponent possible. The variables are $m$ and $n$. $m$ appears squared first, and then at its first power. So we'll chose the squared one. $n$ appears at its first power first, and then cubed, so we'll chose the cubed one.