Number of multiples of 7 up to 1337: \(\left\lfloor\dfrac{1337}7\right\rfloor=191\)
Number of multiples of 11 up to 1337: \(\left\lfloor\dfrac{1337}{11}\right\rfloor=121\)
Number of multiples of 77 up to 1337: \(\left\lfloor\dfrac{1337}{77}\right\rfloor=17\)
This means there are \(191+121-17=295\) distinct multiples of 7 or 11 up to 1337.
The sum of these multiples is
\(\displaystyle\sum_{k=1}^{191}7k+\sum_{k=1}^{121}11k-\sum_{k=1}^{17}77k\)
which can be computed using the well-known formula,
\(\displaystyle\sum_{k=1}^nk=\dfrac{n(n+1)}2\)
So you have
\(\displaystyle\sum_{k=1}^{191}7k+\sum_{k=1}^{121}11k-\sum_{k=1}^{17}77k=7\dfrac{191\times192}2+11\dfrac{121\times122}2-77\dfrac{17\times18}2=197762\)
