# A couple of questions I'm confused about

#### JohnoTheMatho

The following are a couple of questions that I'm getting a bit confused as to how to answer them, any help is appreciated.

1)

2)

#### Archie

1) write a=dp and b=dq. Show that dp divides (ab)/d and that dq also divides (ab)/d.
2) m=ac=bd. Since l=lcd(a,b) divides a and l divides b we get m=lcp=ldq=lk and so l divides m.

Last edited:

#### JohnoTheMatho

How do you show that dp and dq divides (ab)/d? (Thanks for your help for the second one though, I understood that pretty easily)

#### romsek

MHF Helper
How do you show that dp and dq divides (ab)/d? (Thanks for your help for the second one though, I understood that pretty easily)
$a = pd$, $b=qd$

$\dfrac {ab}{d} = \dfrac{pq d^2}{d} = pqd$

$pqd=(pd)q = aq$

$pqd = p(qd) = pb$

and thus $\dfrac{ab}{d}$ is a multiple of both $a$ and $b$

Similar threads