For two natural numbers m and n, let g(m,n) denote the greatest common divisor of m and n. Consider the following in respect of three natural numbers k, m and n:
Ig(m, nk) = g(mn, k).
IIg(m,n)·g(n,k) = g(m,k).
Which of the above is/are correct?

Question

For two natural numbers m and n, let g(m,n) denote the greatest common divisor of m and n. Consider the following in respect of three natural numbers k, m and n:

Ig(m, nk) = g(mn, k).
IIg(m,n)·g(n,k) = g(m,k).

Which of the above is/are correct?

Accepted Answer

Option D: Neither I nor II