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The LCM of two numbers A and B = AB ÷ F, where F is the GCF

For this question, AB = 270 x 9 = 2430

We now need to find a set of paired factors of 2430 such that both numbers are divisible by 9. So, just taking one of the pair as being a multiple of 9 then :-

270 x 9......Yes

135 x 18....Yes

90 x 27......Yes

67.5 x 36....No

54 x 45......Yes.........which is as far as we need to check.

So there are four pairs of numbers satisfying the given conditions : 270 & 9, 135 & 18, 90 & 27 and 45 & 54.

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Q: What two numbers have a GCF of 9 and LCM of 270?
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