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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?
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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?
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Solution
For the shortest height we need to find the LCM of 12 and 18.
The prime factorisations of 12 and 18 are:
12 = 2 × 2 × 3;
18 = 2 × 3 × 3
In these prime factorisations, 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 is 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 × 2 × 3 × 3 = 36
For the shortest height we need to find the LCM of 12 and 18.
The prime factorisations of 12 and 18 are:
12 = 2 × 2 × 3;
18 = 2 × 3 × 3
In these prime factorisations, 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 is 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 × 2 × 3 × 3 = 36
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