7) matt is stacking boxes in two stacks. the first stack has boxes that are 15 inches tall. the second stack…

7) matt is stacking boxes in two stacks. the first stack has boxes that are 15 inches tall. the second stack has boxes that are 10 inches tall. what is the shortest height at which both stacks will have the same height?

7) matt is stacking boxes in two stacks. the first stack has boxes that are 15 inches tall. the second stack has boxes that are 10 inches tall. what is the shortest height at which both stacks will have the same height?

Answer

Explanation:

Step1: Identify the problem type

We need to find the shortest height where both stacks have the same height, which is the least common multiple (LCM) of 15 and 10.

Step2: Prime factorize the numbers

Prime factorization of 15: $15 = 3 \times 5$ Prime factorization of 10: $10 = 2 \times 5$

Step3: Calculate the LCM

To find the LCM, we take the highest power of each prime number that appears in the factorizations. For prime 2: highest power is $2^1$ For prime 3: highest power is $3^1$ For prime 5: highest power is $5^1$ LCM = $2^1 \times 3^1 \times 5^1 = 2 \times 3 \times 5 = 30$

Answer:

The shortest height at which both stacks will have the same height is 30 inches.