Question

Best way to work out planet torrid take 6 years to complete one orbit , planet monde blanc takes 9 years in the year 2035 both planets are lined up perfectly.
How many years will it be before the two worlds are line up again ?

Answer 1

So... hmmm dunno either planet, I assume they're on the solar system and therefore orbiting the same planet, the sun, or whoever.

but, in short, what I can make out is, when do 6 and 9 have the same LCM, least common multiple, or a factor that's common to both 6 and 9, and therefore meet at such.

well, let's do a prime factoring of 6, is 2 and 3 only, ok,
now a prime factoring of 9, is 3 and 3 only, ok.

now, we have 3 as common to both, so, to get an LCD or LCM, we'll use repeated factors but once only for each instance for each.

therefore   $\bf \stackrel{9}{3,3}\qquad \stackrel{6}{2,3}\qquad \stackrel{LCM}{3,3,2}\implies 18$

so, after 18 years.

$\bf \cfrac{6}{18}\implies \cfrac{1}{3}\impliedby \textit{torrid will be orbiting one-third of the way} \\\\\\ \cfrac{9}{18}\implies \cfrac{1}{2}\impliedby \textit{monde blanc will be orbiting half-way}$