Any odd multiple of 30 will be divisible by 5 and 6, but not 4.
The smallest such 4-digit number is 1050 = 5*210 = 6*175 = 30*35.
The largest such 4-digit number is 9990 = 5*1998 = 6*1665 = 30*333.
It must be a multiple of the least common multiple of 5 and 6, which is 2*3*5 = 30. It must not be a multiple of the least common multiple of 4, 5, and 6, which is 2*2*3*5. Thus, there must be only one factor whose value is 2. Any odd multiple of 30 will have only one factor that is 2.
The smallest such 4-digit number is 1050 = 5*210 = 6*175 = 30*35.
The largest such 4-digit number is 9990 = 5*1998 = 6*1665 = 30*333.
It must be a multiple of the least common multiple of 5 and 6, which is 2*3*5 = 30. It must not be a multiple of the least common multiple of 4, 5, and 6, which is 2*2*3*5. Thus, there must be only one factor whose value is 2. Any odd multiple of 30 will have only one factor that is 2.
