LCM of 27 28 30

Question

help!!!!!!!!!!

Answer 1

Do a prime factorization of each number:

 

27 = 3³

28 = 7*2²

30 = 5*3*2     [The 3 and the 2 are already accounted for in the 3³ and 2² terms]

 

The LCM is the product of all unique prime factors, indicated in orange above.  If a prime factor is raised to a power, the LCM includes the highest power term only]

 

LCM = 3³*2²*7*5 = 27*4*7*5 = 3780

Answer 2

The Least Common Multiple (LCM) of some numbers is the smallest number that the numbers are factors of. Take the factors of all 3 numbers here. Find all factors of numbers as shown below. 27 = 3*3*3 28 = 2*2*7 30 = 2*3*5 Now take all unique factors and multiply them together by the maximum number that you see for all the 3 numbers above. Maximum 2's = 2 (28) Maximum 3's = 3 (27) Maximum 5's = 1 (30) Maximum 7's = 1 (28) So LCM = 2*2*3*3*3*5*7 = 3780

Answer 3

Hi Annie, here are different ways to do it:

 

First of all, there are nothing in common from three numbers.

 

27, 28, 30   --->   pick any two and find out its LCM first.

 

As you can see, this LCM must and will end with "0" because of number 30.

 

First option (27, 28)

From this known facts (x, x+1) (27, 28) (27) (28) = 756.  After that, between 756 & 30, the (GCF) of the two is 6.  Only number that these two don't share is 5 (from 30).  Therefore, multiply 756 by 5.  756 x 5 = 3780.  So, final conclusion for LCM (27, 28, 30) is 3780.

 

Second option (27, 30)

From 27 & 30 (3x9  & 3x10) -> (3x9x10), this LCM will be 270.  After that, between 270 & 28, the (GCF) of the two is 2.  Only number that these two don't share is 14 (from 28).  Therefore, multiply 270 by 14.  270 x 14 = 3780.  So, final conclusion for LCM (27, 28, 30) is 3780.

 

Third option (28, 30)

From 28 & 30 (2x14  &  2x15) -> (2x14x15), this LCM will be 420.  After that, between 420 & 27, the (GCF) of the two is 3.  Only number that these two don't share is 9 (from 27).  Therefore, multiply 420 by 9.  420 x 9 = 3780.  So, final conclusion for LCM (27, 28, 30) is 3780.

 

 

Good luck to you.  I hope you understand how I it.

 

 

Here is a little known fact about multiples:

 

Whenever you multiply by 5 with any even number will give you new number that ends with 0.  But if you multiply by 5 with any odd number will give you new number that ends with 5.

 

Answer 4

Hello, Glendora

 

The best way to do this is to find the prime factors of the numbers:

27:3,3,3

28:2,2,7

30:2,3,5

 

So, we need at least three 3's, at least two 2's, one 5 and one 7. The multiply 2*2*3*3*3*5*7= 3,780

 

You can also do this the long way, by actually getting all the multiples until you reach the first they have in common.

27: 27, 54, 81,108,135, .............................3780 

28: 28, 56, 84, 112,...................................3780

30:30,60, 90, 120, 150, 180, 210, 240, .......3780

 

Glad to help, and have fun doing all the multiples :).

 

D. Y. Taylor