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 beĀ divisible by both 6 and 7. The LCM of these is 42. It means thatĀ 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.
TheĀ smallest three-digit number is 100. When we divide 100 by 42, then the remainder will beĀ 16. So we need to add (42-16) in 100.
So A = 100+(42-16)
A = 100+26
A =Ā 126
B is the largest four-digit number divisible by both 6 and 7.
TheĀ 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) =Ā 9996-126
=Ā 9870
Create a FREE account and get:
