Math Problem Statement
What is the side length of the smallest square design that could be formed from tiles measuring 6 cm by 15 cm ? Assume the tiles cannot be cut.
Solution
To find the side length of the smallest square that can be formed using tiles measuring 6 cm by 15 cm without cutting the tiles, we need to determine the least common multiple (LCM) of the two dimensions: 6 cm and 15 cm.
This is because the side of the square must be a multiple of both 6 cm and 15 cm to ensure the tiles fit perfectly.
Step-by-Step Calculation:
- Prime factorization of 6:
- Prime factorization of 15:
- LCM of 6 and 15:
The LCM is found by taking the highest powers of all prime factors present:
Thus, the side length of the smallest square that can be formed is 30 cm.
Conclusion:
The smallest square has a side length of 30 cm.
Would you like further clarification or details on any part of this solution?
Here are 5 related questions for you to consider:
- How many tiles would be needed to cover the 30 cm square?
- How do you find the greatest common divisor (GCD) of two numbers?
- What is the difference between LCM and GCD?
- How can the concept of tiling be extended to three dimensions?
- Can a rectangular shape other than a square be formed with the same tiles?
Tip: When solving problems involving fitting shapes, always check for the LCM or GCD to find the smallest or largest fitting dimensions.
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Math Problem Analysis
Mathematical Concepts
Least Common Multiple (LCM)
Prime Factorization
Geometry (Tiling)
Formulas
LCM(a, b) = (a * b) / GCD(a, b)
Theorems
LCM Theorem
Suitable Grade Level
Grades 6-8