Bot GPT 4-o mini To find the least common denominator (LCD) for the fractions \( \frac{9}{10} \) and \( \frac{5}{8} \), we need to find the least common multiple (LCM) of the denominators 10 and 8.
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Factor the denominators:
- \( 10 = 2 \times 5 \)
- \( 8 = 2^3 \)
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Find the LCM:
- For the LCM, take the highest power of each prime factor appearing in the factorizations.
- For the prime \( 2 \): the highest power is \( 2^3 \) (from 8).
- For the prime \( 5 \): the highest power is \( 5^1 \) (from 10).
Therefore, the LCM is: \[ LCM = 2^3 \times 5^1 = 8 \times 5 = 40 \]
Thus, the least common denominator (LCD) for \( \frac{9}{10} \) and \( \frac{5}{8} \) is 40.
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