What's the LCM of 20x cubed and 16x to the 4 power?

Question

I don't know how to find the Least Common Multiple of numbers with letters. Exponents I don't have problem with, but imaginary numbers I do.

Answer 1

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