After that prelude, the question is this:Let $\displaystyle q_1=\frac{m_1}{n_1}$ and $\displaystyle q_2= \frac{m_2}{n_2}$ be positive rational numbers. We define the lowest common multiple of $\displaystyle q_1$ and $\displaystyle q_2$, lcm $\displaystyle (q_1,q_2)$, to be the smallest positive rational number q such that $\displaystyle q=Mq_1=Nq_2$ for some positive integers M and N.

I know that $\displaystyle hcf(m,n)( lcm (m,n))=mn$ but I have no idea where to go from here.Find a formula for $\displaystyle lcm (q_1,q_2)$. Your answer can include expressions of the form lcm(m,n) and hcf(m,n) where m and n are integers.

Can someone point me in the right direction?