Need helpwith this

Question

pads of paper come 4 to a box, pencils come 27 to a box and erasers come 12 to a box. what is the least number of kits that can be made with paper, pencils and erasers with no supplies left over??

Answer 1

Hi Linda,

 

David's answer is correct.

 

We need to find a number in which the number of pads, the number of pencils, and the number of erasers are the SAME number.  The Lowest Common Multiple (LCM) is that number.

 

The process for arriving at the LCM is by breaking down each number into its prime factors and then taking the product of each of the common prime factors from the breakdowns and the unique (left over) prime factors from any of the breakdowns.

 

Below is a link to a diagram which visually shows the prime factor breakdown of each number and how the LCM was built from the prime factors of each number:

 

https://dl.dropbox.com/s/hvnskhvllgoj3lg/LCM_from_Prime_Factors.png?raw=1

 

God bless, Jordan.

 

Answer 2

In order to use all the supplies, the number of kits made must be a multiple of 4 (for paper pads), a multiple of 27 (for pencils) and a multiple of 12 (for erasers).  The least number that satisfies this is called the Least Common Multiple (LCM).

 

It must have factors that include the factors of 4 (2,2), the factors of 27 (3,3,3) and the factors of 12 (2,2,3).

The least number that does that has factors of  (2,2,3,3,3), which is 108.