Prime Factorization and exponents

Question

A warehoyse has boxes that are 18 inches tall and other boxes that are 30 inches tall.

A. If 18 inches boxes are stacked next to 30 inches boxes, what is the liwest height at wich the two stacks be the same height?

 

B. How many boxes wil there be in each stack?

Answer 1

Hello Cecilia,

What we’re looking for is the LCM (Least Common Multiple). When you’re adding fractions it’s called the Lowest Common Denominator.

Some multiples of 18 are: 36, 54, 72, 90
Some multiples of 30 are: 60, 90, 120

So, we can see that both 18 and 30 have a common multiple of 90, which answers the first question: 90 inches is the lowest height which the two stacks will be the same height.

For part B: We will need 5 of the 18 inch boxes (5 x 18 = 90), and we’ll need only 3 of the 30 inch boxes (3 x 30 = 90) for the stacks to be the same height.

Hope this Helps,
John B.

Answer 2

18 = 2 x 3 x 3

30 = 2 x 3 x 5

 

When the stack is the same height, you must have all the factors for each number so : 2 x 3 x 3 x 5 = 90

 

that will be 5 boxes of the 18 inch tall boxes

and 3 of the 30 inch tall boxes