if you mean 20x^3 and 16x^4 then
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 2 * 2 * 5 (to make 20) and 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^3 and x^4 is x^4
the lcm of the whole thing is 80x^4
if you mean (20x)^3 and (16x)^4 then:
(20x)^3 = 8000x^3
(16x)^4 = 65536x^4
first, the numbers
8000 = 2^6 * 5^3
65536 = 2^16
the lcm is 2^16 * 5^3 because 2^16 * 5^3 contains 2^6 * 5^3 (to make 8000) and 2^16 (to make 65536)
2^16 * 5^3 = 8192000
now the x's
the lcm of x^4 and x^3 is x^4
the lcm of the whole thing is 8192000x^4