To find the LCM and GCF of a set of numbers it is best if we first write them as product of prime factors.

Now 27 = 3*3*3

90 = 3*3*5*2

84 = 3*2*2*7

For the greatest common factor GCF take the product of the largest set of common factors between the three numbers. We see that only 3 is common to all the three numbers. This gives the GCF as 3.

The Least Common Multiple is the product of all the factors of the numbers; this is 3*3*3*5*2*2*7 = 3780.

**Therefore for the numbers 27, 90 and 84 the LCM is 3780 and the GCF is 3.**

The GCF of 27, 90, and 84.

27 = 3*3*3.

90 = 2*3*3*5.

84=2*2*3*7.

So the greatest common factors to all the 3 numbers is 3.

LCM:

We do the LCM division:

3 ) 27, 90, 84

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3) 9, 30, 28

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3) 3, 10, 28

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2) 3, 5, 14

There no more division as two or more numbers are not divisible by the same numbers.

So LCM = 3*3*2*3*514 = 2^2*3^3*5*7 = 3780

So LCM = 3780 and GCF = 3.