To find the least common denominator (LCD) of the fractions \( \frac{2}{5} \) and \( \frac{1}{6} \), we first need to determine the denominators of the fractions, which are 5 and 6.
The next step is to find the least common multiple (LCM) of these two numbers.
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Identify the prime factorization:
- The prime factorization of 5 is \( 5^1 \).
- The prime factorization of 6 is \( 2^1 \times 3^1 \).
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Find the LCM by taking the highest power of each prime factor:
- The primes in consideration are 2, 3, and 5.
- The highest power of 2 is \( 2^1 \).
- The highest power of 3 is \( 3^1 \).
- The highest power of 5 is \( 5^1 \).
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Calculate the LCM: \[ \text{LCM} = 2^1 \times 3^1 \times 5^1 = 2 \times 3 \times 5 \] \[ 2 \times 3 = 6 \] \[ 6 \times 5 = 30 \]
Thus, the least common denominator (LCD) of \( \frac{2}{5} \) and \( \frac{1}{6} \) is \( \boxed{30} \).