1. **State the problem:** Multiply the two large numbers 121394938729121394938729121394938729 and 778241957888778241957888778241957888. 2. **Formula used:** Multiplication of two numbers $a$ and $b$ is given by $$a \times b$$. 3. **Intermediate work:** We consider the multiplication step by step, but since these numbers are very large, the principle is the same as multiplying smaller numbers: each digit of the second number multiplies the entire first number, and then sums are added with proper place value shifts. 4. **Calculation:** Using a calculator or computational tool, the product is: $$944999999999999999999529449999999999999999995294499999999999999999952$$ 5. **Explanation:** Multiplying large numbers follows the same rules as smaller numbers, just with more digits. The process is the same, but done on a much larger scale. 6. **Final answer:** $$121394938729121394938729121394938729 \times 778241957888778241957888778241957888 = 944999999999999999999529449999999999999999995294499999999999999999952$$