J JohnoTheMatho Apr 2016 3 0 London Apr 5, 2016 #1 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)

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)

A Archie Dec 2013 2,002 757 Colombia Apr 5, 2016 #2 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: Apr 5, 2016

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.

J JohnoTheMatho Apr 2016 3 0 London Apr 5, 2016 #3 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)

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 Nov 2013 6,836 3,079 California Apr 5, 2016 #4 JohnoTheMatho said: 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) Click to expand... $a = pd$, $b=qd$ $\dfrac {ab}{d} = \dfrac{pq d^2}{d} = pqd$ $pqd=(pd)q = aq$ $pqd = p(qd) = pb$ and thus $\dfrac{ab}{d}$ is a multiple of both $a$ and $b$

JohnoTheMatho said: 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) Click to expand... $a = pd$, $b=qd$ $\dfrac {ab}{d} = \dfrac{pq d^2}{d} = pqd$ $pqd=(pd)q = aq$ $pqd = p(qd) = pb$ and thus $\dfrac{ab}{d}$ is a multiple of both $a$ and $b$