Question

Find H.C.F. of $576$ and $720$ if their L.C.M. is $2880$.

Answer 1

A relation works for two numbers and their L.C.M., H.C.F.
Product of two numbers = L.C.M. of two numbers $\times$H.C.F. of two numbers
$576\times 720=2880\times$H.C.F.
H.C.F. $=\frac{576\times 720}{2880}=\frac{24\times 24\times 72}{288}=\frac{24\times 72}{12}=2\times 72=144$
So, the H.C.F. of $576\mathrm{and}720\mathrm{is}144$.