Question

The least common multiple of 54c^2de^3 and 38c^4 is _____.
a) 342c^2
b) 1,026c^4de^3
c) 342c^4de^3
d) 1,026c^4

Answer 1

54c^2de^3 ? You mean 54c^2 and de^3 ?

Answer 2

Yeah.

Answer 3

Start with the number parts: 54 and 38
54 = 2 x 3 x 3 x 3 = 2 x 3^3
38 = 2 x 19
For the LCM you need to use factors that are common to both numbers or not common to both numbers with the higher exponent.
2 is common to both, so pick it: 2
3 is only in 54, and you have 3^3, so use 3^3
19 is only in 38, so use it too
The number part then is: 2 x 3^3 x 19 = 1026

With the variables, do the same. Use all the variables and pick the higher powers.
Between c^2 and c^4 pick c^4
Between d and no d use d
Between e^3 and no e, use e^3
So the variable part is c^4de^3

Once you put it all together, you get 1026c^4de^3