What are the LCM and GCF of 27, 90 and 84?  

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

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

----------------------------

3)  9,   30,    28

-----------------------------

3) 3,    10,     28

-----------------------------

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.

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