The LCM of two numbers is 250 times their HCF. The sum of LCM and HCF is 4016. If one of the numbers  is 640, then what is the other numbers?

100

L.C.M. = 250 × H.C.F.

L.C.M. + H.C.F. = 4016

250 × H.C.F. + H.C.F. = 4016

                   251 H.C.F. = 4016

                         H.C.F. = \(\frac{4016}{251}\) = 16

We know that,

                   HCF × LCM = product of two numbers

                     16 × 250 × 16 = 640 × ?

                                        ? = 100