There are 3 numbers $a,b,c$ such that $HCF(a,b)=l,HCF(b,c)=m$ and $HCF(c,a)=n$. $HCF(l,m)=HCF(l,n)=HCF(n,m)=1$. Find LCM of $a, b, c$. My solution approach for this problem was to use the relationship formula between LCM and HCF of three numbers which is 
$$LCM(p,q,r)=\frac{pqr \times HCF(p,q,r)}{HCF(p,q) \times HCF(q,r) \times HCF(r,p)}$$and upon using this formula I get 
$$LCM(a,b,c)=\frac{abc \times HCF(a,b,c)}{lmn}$$
But I am not able to figure out the the value of $HCF(a,b,c)$.
Can someone please help on this?
Thanks in advance !!!

We can express a, b and c as
a=ln(a') , b=lm(b') and c=mn(c')
As the HCF(a,b)=l , therefore
HCF(lna',lmb') = l , therefore
HCF(na',mb')=1 . Now as m,n are co-prime , HCF(a',b')=1.
Similarly we can find that HCF(a',b',c')=1 , therefore HCF(a,b,c)=1
Therefore , with your formulae , LCM(a,b,c) becomes abc/lmn
