Question

how do you find the least common multiple of these two expressions. 10x^5v^8 and 25x^4v^7u^2

Answer 1

$10x^{5} v^{8}= 1*2*5*x*x*x*x*x*v*v*v*v*v*v*v*v \\ 25 x^{4} v^{7} u^{2}=1*5*5*x*x*x*x*v*v*v*v*v*v*v*u*u$
Underline all the numbers which are common in both the factorisations. Write them down:
$5 x^{4} v^{7}$
There, you have your LCM of both the expressions.

Answer 2

$10x^5v^8=5x^4v^7\cdot2xv\\\\25x^4v^7u^2=5x^4v^7\cdot5u^2\\\\LCM(10x^5v^8;\ 25x^4v^7u^2)=5x^4v^7\cdot2xv\cdot5u^2=50x^5v^8u^2$