Greatest common factor (or denominator) is 6, least common multiple is 180
hmm (note:
I spent like 30 mins trying to use a math only of finding the values
but it didn't work so I did a force brute and elimination method
explained below)
so a and b must be multiples of 6 so list all the multiples of 6 wait 180=6*30
and 30's factors are 1,2,3,5,6,10,15,30 so only list the numbers that
are the result of multiplying 6 and any of those numbers in that list
(so we can have the lcm of 180) so 6*1=6 6*2=12 6*3=18 6*5=30 6*6=36 6*10=60 6*15=90 6*30=180 these are our possible candidates for the 2 numbers now we must find the pair that has a GCD of only 6
doing the math is long and tedious so do it yourself (trial and error)
we see that our choices that fulfill both requirements (GCD of 6 and LCM of 180) are 90&12 60&18 30&36 sum them to find the least one
6+5=11+5=16+5=21 3+6=9+6=15+6=21 It will take Marco and Sophie 3 hours to get the same amount of money. The amount of money they will have will be $21.
