In [1]:
import sympy as sym
import numpy as np
import math

from IPython.display import display, Math
from sympy.abc import w,x,y,z,a,b,c,d
sym.init_printing()
In [2]:
sym.gcd(a*c,b*c)
Out[2]:
$$c$$
In [3]:
sym.gcd(a,b)
Out[3]:
$$1$$
In [4]:
a = 15
b = 6
c = 3

sym.gcd(a*c,b*c)
Out[4]:
$$9$$
In [5]:
sym.gcd(a,b)
Out[5]:
$$3$$
In [6]:
n = 10
m = 15

gcdMat = np.zeros([n,m])+99
gcdMat
Out[6]:
array([[99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99.,
        99., 99.],
       [99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99.,
        99., 99.],
       [99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99.,
        99., 99.],
       [99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99.,
        99., 99.],
       [99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99.,
        99., 99.],
       [99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99.,
        99., 99.],
       [99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99.,
        99., 99.],
       [99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99.,
        99., 99.],
       [99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99.,
        99., 99.],
       [99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99., 99.,
        99., 99.]])
In [7]:
for rowi in range(0,n):
    for coli in range(0,m):
        gcdMat[rowi,coli] = math.gcd(rowi+1,coli+1)
        
sym.sympify(gcdMat)
Out[7]:
$$\left[\begin{array}1.0 & 1.0 & 1.0 & 1.0 & 1.0 & 1.0 & 1.0 & 1.0 & 1.0 & 1.0 & 1.0 & 1.0 & 1.0 & 1.0 & 1.0\\1.0 & 2.0 & 1.0 & 2.0 & 1.0 & 2.0 & 1.0 & 2.0 & 1.0 & 2.0 & 1.0 & 2.0 & 1.0 & 2.0 & 1.0\\1.0 & 1.0 & 3.0 & 1.0 & 1.0 & 3.0 & 1.0 & 1.0 & 3.0 & 1.0 & 1.0 & 3.0 & 1.0 & 1.0 & 3.0\\1.0 & 2.0 & 1.0 & 4.0 & 1.0 & 2.0 & 1.0 & 4.0 & 1.0 & 2.0 & 1.0 & 4.0 & 1.0 & 2.0 & 1.0\\1.0 & 1.0 & 1.0 & 1.0 & 5.0 & 1.0 & 1.0 & 1.0 & 1.0 & 5.0 & 1.0 & 1.0 & 1.0 & 1.0 & 5.0\\1.0 & 2.0 & 3.0 & 2.0 & 1.0 & 6.0 & 1.0 & 2.0 & 3.0 & 2.0 & 1.0 & 6.0 & 1.0 & 2.0 & 3.0\\1.0 & 1.0 & 1.0 & 1.0 & 1.0 & 1.0 & 7.0 & 1.0 & 1.0 & 1.0 & 1.0 & 1.0 & 1.0 & 7.0 & 1.0\\1.0 & 2.0 & 1.0 & 4.0 & 1.0 & 2.0 & 1.0 & 8.0 & 1.0 & 2.0 & 1.0 & 4.0 & 1.0 & 2.0 & 1.0\\1.0 & 1.0 & 3.0 & 1.0 & 1.0 & 3.0 & 1.0 & 1.0 & 9.0 & 1.0 & 1.0 & 3.0 & 1.0 & 1.0 & 3.0\\1.0 & 2.0 & 1.0 & 2.0 & 5.0 & 2.0 & 1.0 & 2.0 & 1.0 & 10.0 & 1.0 & 2.0 & 1.0 & 2.0 & 5.0\end{array}\right]$$