Question

Boxes that are 12 inches tall are being stacked next to boxes that are 18 inches tall. What is the shortest height at which the two stacks will be of same height? [4 MARKS]

Answer 1

Concept: 1 Mark
Steps: 2 Marks
Answer: 1 Mark

For the shortest height, we need to find the LCM of 12 and 18

The prime factorization of 12 and 18 are:

12 = 2 $\times$ 2 $\times$ 3;

18 = 2 $\times$ 3 $\times$ 3

In these prime factorizations, the maximum number of times the prime factor 2 occurs is two; this happens for 12.
Similarly, the maximum number of times the factor 3 occurs is two; this happens for 18.
The LCM of the two numbers are the product of the prime factors counted the maximum number of times they occur in any of the numbers.
Thus, in this case LCM = 2 $\times$ 2 $\times$ 3 $\times$ 3 = 36.
Hence, the shortest height for which the two stacks will have the same height is 36 inches.