Quick way (Probably too much horizontal space though):
n=int(input('Please enter a positive integer between 1 and 15: '))
for row in range(1,n+1):
for col in range(1,n+1):
print(row*col, end="")
print()
Better way:
n=int(input('Please enter a positive integer between 1 and 15: '))
for row in range(1,n+1):
print(*("{:3}".format(row*col) for col in range(1, n+1)))
And using f-strings (Python3.6+)
for row in range(1, n + 1):
print(*(f"{row*col:3}" for col in range(1, n + 1)))
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