To simplify the expression \( \frac{123}{34} \times \frac{12}{34} \), you can first multiply the numerators together and the denominators together:
\[ \frac{123 \times 12}{34 \times 34} \]
Calculating the products:
- \( 123 \times 12 = 1476 \)
- \( 34 \times 34 = 1156 \)
Now, substitute these values back into the fraction:
\[ \frac{1476}{1156} \]
Next, we can simplify this fraction. The greatest common divisor (GCD) of 1476 and 1156 is 4:
\[ \frac{1476 \div 4}{1156 \div 4} = \frac{369}{289} \]
Thus, the simplified form of \( \frac{123}{34} \times \frac{12}{34} \) is:
\[ \frac{369}{289} \]