Let the number of coins be - N

Then, N - 1 is a multiple of 1, 2, 3, 4, 5, 6 but not 7. The LCM of 1, 2, 3, 4, 5, 6 is 60

Again N is a multiple of 7.

So, N should be any number which is a multiple of 7 and N - 1 is a multiple of 60. So upon finding the multiples of 60 and adding 1 to them we find 60 * 5 = 300 + 1 = 301 is such a number.

Therefore N = 301.