Two coils are said to be magnetically coupled, if full or a part of the flux produced by one links with the other. Let L1 and L2 be the self-inductances of the coils and M be their mutual inductances, then k=L1L2M
When 100% flux produced by one coil links with the other, then mutual inductance between the two is maximum and is given by M=L1L2
In that case, k=1 (unity)
Note: When there is no common flux between the two coils, they are said to be magnetically isolated. In this case, k=C and M=0. In practice k lies between O and 1.