Red cups that are 10 inches tall are being stacked next to blue cups that are 14 inches tall.
What is the shortest height at which the two stacks would be the same height?

24 inches

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55 inches

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120 inches

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70 inches

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Solution

The correct option is D 70 inches
To get the required lengths of the two stacks, we need to find the LCM of the heights of the cups.

Let's find the LCM of 10 and 14 using the prime factorization method.

The prime factors of 10 are: 2 × 5
The prime factors of 14 are: 2 × 7

Thus, the least common multiple of 10, 14 is: 2 × 5 × 7 = 70

Hence, the shortest height at which stacks would be the same height is 70 inches.

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Red cups that are 10 inches tall are being stacked next to blue cups that are 14 inches tall. What is the shortest height at which the two stacks would be the same height?

Red cups that are 10 inches tall are being stacked next to blue cups that are 14 inches tall.
What is the shortest height at which the two stacks would be the same height?