# What 4 digit # can be divisible into 5 and 6 but not 4?

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.
thanked the writer.
Suppose you have four numbered tiles, one with a 3 on it, one with a 4, one with a 5, and one with a 6.
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