Suppose that the smallest number is X and we have to increase it by 5 i.e., we will add 5 to it.
X+5, and it should be divisible by 8, 11 and 24.
To ensure that (X+5) is divisible by all three divisors i.e., 8, 11 and 24, we have to take the LCM of 8, 11 and 24.
If the above question is written in the form of an equation, it would look like this:
X+5 = LCM of 8, 11, 24
Lcm of 8, 11, 24 = D; D represents the LCM of 8, 11, 24
So, in order to make X divisible by D, transpose 5 from the left-hand side to the right-hand side because the value of X is unknown, but the value of D which is the LCM of 8, 11, and 24 will very soon be calculated.
X=D-5; and this is the answer.
Firstly find D, the LCM of 8, 11, 24.
The common factors will be taken only once to find the LCM of 8, 11, and 24
24x11x1=264 is the LCM of 8, 11, and 24
Where 24=2x2x2 x3
So the LCM of 8, 11, 24 or the value of D is =264
Hence the option (b) is correct and the answer is 259.
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