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Find how many 3 digits numbers satisfy all the following conditions

if it is divided by 2, the remainder is 1, if it is divided by 3, the remainder is 2, if it is divided by 4, the remainder is 3, if it is divided by 5, the remainder is 4, if it is divided by 8, the remainder is 7,

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Let the number N satisfy the conditions. Let x, y, z, w, v be some integers.

N can be written as 2 x + 1 or 2 x - 1. so let us write N as

N = 2 x - 1 N = 3 y - 1 or 3 x' + 2 where x' = y -1 N = 4 z - 1 or 4 z' + 3 where z' = z - 1 N = 5 w - 1 or 5 w' + 4 N = 8 v - 1 or 8 v' + 7

So N + 1 = 2 x = 3 y = 4 z = 5 w = 8 v

N+1 is a multiple of 2,3,4,5, and 8

N+1 is a multiple of lcm of them.

LCM = 2*3*2*5*2 = 120

Three digit multiples of 120 are 120, 240, 360, 480, 600, 720, 840, 960