Find the sum of all common multiples of 28 and 63 up to 550.

To find the sum of all common multiples of given numbers, remember what the least common multiple is;

To find the least common multiple of several numbers, you need to decompose these numbers into prime factors and find the product of all the resulting prime factors, taking each of them with the largest exponent;

We have 28 = 4 * 7; 63 = 7 * 9;

Then we take all prime factors that are included in the decomposition of at least one of these numbers:

We get: 4 * 7 * 9 = 252;

The sum of common multiples of 28 and 63, not exceeding 550, according to the condition of the task, will be equal to: 252 + 504 = 756.