Answer: x = 27
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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
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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.