AMC 8 1987 Problem 9

When finding the sum $\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}$, the least common denominator used is $\text{(A)}\ 120 \text{(B)}\ 210 \text{(C)}\ 420 \text{(D)}\ 840 \text{(E)}\ 5040$