l:m = 3/2 : 7/4 = 6 : 7
m:n = 7/3 : 21/5 = 35 : 63
l:n = 10 : 21
to do l:m:n we need the letter (m) that's in both l:m and m:n to be the same
l:m = 6 : 7 = 30 : 35
m:n = 35 : 63
so l:m:n = 30 : 35 : 63
does that fit with l:n = 10 : 21 ?
l:n = 10 : 21 = 30 : 63
yes, it fits
Solution: l:m:n = 30 : 35 : 63