Question
Frame carpenters typically work with measurements as small as \( \frac{1}{16} \) inch. Trim carpenters and cabinetmakers may work with measurements as small as \( \frac{1}{64} \) inch. Find the lowest common denominator for the fractions \( \frac{6}{16} \) and \( \frac{12}{64} \). Your answer should be a whole number, representing the lowest common The lowest common denominator for the two fractions is
Ask by Mckenzie Donnelly. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The lowest common denominator for the fractions \( \frac{6}{16} \) and \( \frac{12}{64} \) is **64**.
Solution
To find the lowest common denominator (LCD) for the fractions 6/16 and 12/64, we need to find the least common multiple (LCM) of the denominators 16 and 64.
Step 1: List the multiples of each denominator.
• Multiples of 16: 16, 32, 48, 64, 80, …
• Multiples of 64: 64, 128, 192, …
Step 2: Identify the smallest common multiple.
The first common multiple is 64.
Thus, the lowest common denominator for the two fractions is 64.
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Simplify this solution The Deep Dive
To find the lowest common denominator (LCD) of \( \frac{6}{16} \) and \( \frac{12}{64} \), we start by determining the denominators: 16 and 64. The multiples of 16 are 16, 32, 48, 64, and so on. The multiples of 64 are 64, 128, and so forth. The smallest common multiple of both numbers is 64. Thus, the lowest common denominator for the two fractions is **64**. Now that we have the LCD, it’s vital to remember that converting fractions to a common denominator can help you easily add or compare them. So, if you need to work with these fractions in future calculations, knowing how to find the LCD will save you time and potential miscalculations!
