Answer:
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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.