first, the numbers
20 = 2 * 2 * 5
16 = 2 * 2 * 2 * 2
the lcm is 2 * 2 * 2 * 2 * 5 because 2 * 2 * 2 * 2 * 5 contains a 2 * 2 * 5 (to make 20) and a 2 * 2 * 2 * 2 (to make 16)
2 * 2 * 2 * 2 * 5 = 80
the lcm of 20 and 16 is 80
now the x's
the lcm of x^2 and x^5 is x^5
note: x^5 = x^2 * x^3
now the y's
the lcm of y^4 and y^4 is y^4
the lcm of the whole thing is 80(x^5)(y^4)