If A is the smallest three-digit number divisible by both 6 and 7 and B is the largest four-digit number divisible by both 6 and 7, then what is the value of (B - A)?

LCM of (6, 7) = 42

6 = $$2\times3$$

7 = 7

As per the information given in the question, the value of both A and B will be divisible by both 6 and 7. The LCM of these is 42. It means that the value of both A and B will be the multiple of 42.

If A is the smallest three-digit number divisible by both 6 and 7.

The smallest three-digit number is 100. When we divide 100 by 42, then the remainder will be 16. So we need to add (42-16) in 100.

So A = 100+(42-16)

A = 100+26

A = 126

B is the largest four-digit number divisible by both 6 and 7.

The largest four-digit number is 9999. When we 9999 by 42, then the remainder will be 3. So we need to subtract 3 from 9999.

So B = 9999-3

B = 9996

Value of (B - A) = 9996-126

= 9870