The least number which when divided by 16, 18, 20 and 25 leaves 4 as remainder in each case but when divided by 7 leaves no remainder.

LCM of 16, 18, 20, 25 = 3600. The number leaves remainder 4 when divided by these, so it is of the form 3600k + 4. We need this to be divisible by 7: 3600k + 4 ≡ 0 (mod 7). Since 3600 = 7×514 + 2, we have 3600 ≡ 2 (mod 7). So: 2k + 4 ≡ 0 (mod 7), giving 2k ≡ 3 (mod 7), so k ≡ 5 (mod 7). The smallest such k is 5, giving the number: 3600×5 + 4 = 18004, which is divisible by 7 (18004/7 = 2572).