My score: $$ 27 / 122 \mathrm{pts}(22.13 \%) $$ 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

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To find the lowest common denominator (LCD) for the fractions $$ \frac{6}{16} $$ and $$ \frac{12}{64} $$, we need to determine the least common multiple (LCM) of the denominators 16 and 64.

### Step 1: Factor the denominators
- The prime factorization of $$ 16 $$ is:
  $$
  16 = 2^4
  $$
- The prime factorization of $$ 64 $$ is:
  $$
  64 = 2^6
  $$

### Step 2: Determine the LCM
To find the LCM, we take the highest power of each prime factor that appears in the factorizations:
- For the prime factor $$ 2 $$, the highest power is $$ 2^6 $$ (from 64).

Thus, the LCM of 16 and 64 is:
$$
\text{LCM} = 2^6 = 64
$$

### Conclusion
The lowest common denominator for the fractions $$ \frac{6}{16} $$ and $$ \frac{12}{64} $$ is $$ 64 $$.
The lowest common denominator for the fractions $$ \frac{6}{16} $$ and $$ \frac{12}{64} $$ is 64.

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