1. **State the problem:** We need to find the sum of the fractions $\frac{1}{628} + \frac{1}{763} + \frac{1}{1469}$.\n\n2. **Formula and approach:** To add fractions, we find a common denominator and then add the numerators. The common denominator is the least common multiple (LCM) of the denominators.\n\n3. **Find the LCM of 628, 763, and 1469:**\n- Prime factorize each denominator:\n - $628 = 2^2 \times 157$\n - $763$ is prime\n - $1469$ is prime\n- Since 763 and 1469 are prime and do not share factors with 628, the LCM is $628 \times 763 \times 1469$.\n\n4. **Calculate the LCM:**\n$$\text{LCM} = 628 \times 763 \times 1469 = 703,422,964$$\n\n5. **Rewrite each fraction with the common denominator:**\n$$\frac{1}{628} = \frac{763 \times 1469}{703,422,964} = \frac{1,121,447}{703,422,964}$$\n$$\frac{1}{763} = \frac{628 \times 1469}{703,422,964} = \frac{922,532}{703,422,964}$$\n$$\frac{1}{1469} = \frac{628 \times 763}{703,422,964} = \frac{478,964}{703,422,964}$$\n\n6. **Add the numerators:**\n$$1,121,447 + 922,532 + 478,964 = 2,522,943$$\n\n7. **Final sum:**\n$$\frac{2,522,943}{703,422,964}$$\n\n8. **Simplify the fraction if possible:**\n- Check for common factors between numerator and denominator. Since the numerator is much smaller and the denominator is a product of distinct primes, the fraction is already in simplest form.\n\n**Answer:**\n$$\frac{1}{628} + \frac{1}{763} + \frac{1}{1469} = \frac{2,522,943}{703,422,964}$$