Largest Possible GCD of 7 Distinct Integers

Let the 7 distinct integers be $m a_1, m a_2, \dots, m a_7$ where $m$ is GCD. $m(a_1 + a_2 + \dots + a_7) = 1740$. Minimum sum of 7 distinct positive integers $1+2+3+4+5+6+7 = 28$. Next smallest distinct sum = $1+2+3+4+5+6+8 = 29$. $1740 = 60 \times 29$. Since 29 is prime, $m = 60$ is the maximum GCD.