Number Theory
# Greatest Common Divisor / Lowest Common Multiple

$\text{lcm}(1,77) + \text{lcm}(2,77) + \text{lcm}(3,77) + \cdots + \text{lcm}(77,77) = \, ?$

**Notation**: $\text{lcm}(a,b)$ denote the Lowest Common Multiple of $a$ and $b$.

When 2017 is divided by a 2-digit number, what is the largest possible remainder?

**Bonus:** Generalize this problem.

Find the sum of all integers $k$ with $1\leq k\leq 2015$ and $\gcd(k,2015)=1$.