X is a natural number with
GCF(x, 36) = 9 and LCM(x, 36)
36) =108
Find x.

Work Shown:

x = some natural number

G = GCF(x,36)

L = LCM(x,36)

We can tie together the LCM and GCF like so

L = (x*36)/G

L = (x*36)/9

L = (36/9)*x

L = 4x

Whatever the value of x is, the LCM is 4 times larger.

Since we're told the LCM is 108, we can then say,

L = 108

4x = 108

x = 108/4

x = 27

Check:

GCF(x,36) = GCF(27,36) = 9, since 36 = 9*4 and 27 = 9*3, indicating that 9 is the largest shared factor

LCM(x,36) = LCM(27,36) = 108

LCM(x,36) = (x*36)/GCF = (x*36)/9 = (27*36)/9 = 972/9 = 108

This confirms we have the right answer.