2025/010) What should be the middle number if the L.C.M. of 3 consecutive even numbers is 4896?

 Let us factor $4896 = 48 * 102 = 2^5 * 3^2 * 17$

Because LCM is 4896 any one of the numbers should be multiple of $q^5=32$ one should be multiple of $17$ and one must be a multiple of $3^2=9$ and it must be remembered that  one number may satisfy one or more criteria. And no number can have a factor other than 2 , 3, of 147 7 and any power of these 3 more than as specified above

Let us try with $2^5$ or 32 say a

If 32 is there it has to be first number as 30 cannot there ( 5 is a factor)

So let us consider $32,34,36$. 34 is multiple of 17 and 36 is multiple of 9.

Le us take valid multiple of 32 that is $32 * 3$ 2 adjacent numbers are 94 and 98 not permissible as 94 has a factor  47 and 98 has factor 7

similarly we can rule out others

So the 3 numbers are $32,34,36$ and middle number is 34.