Find the greatest $7$ digit number which is divisible by $15,25$ and $35$ exactly.

The correct option is B $9999675$

To find: greatest 7 digit number which is divisible by 15, 25, 35.

Now,

Factors of $15=3\times 5$

Factors of $25=5\times 5$

Factors of $35=5\times 7$

LCM of $15,25,35$ $=3\times 5\times 5\times 7=$ $525.$

We know that the Greatest $7$ digit number is $9999999$

On dividing the above number by $525$ it leaves a reminder of $324$

That is, $9999999=525\times 19047+324$

So, the number is $9999999-324=9999675$

Therefore, $B$ is the correct answer.