Question

Find the greatest six digit number exactly divisible by $24,15$ and $36$

Answer 1

Now, we know that the greatest six digit number is $9,99,999$

Now, the greatest six digit number which is divisible by $24,15$ and $36$ should be a multiple of LCM of $24,15,36$.

$\begin{array}{cc}2& 24,15,36\\ 2& 12,15,18\\ 2& 6,15,9\\ 3& 3,15,9\\ 3& 1,5,3\\ 5& 1,5,1\\ & 1\end{array}$

LCM $=2\times 2\times 2\times 3\times 3\times 5=360$

Now,

Thus, the remainder obtained is $279$

Hence, the largest six digit number divisible by $24,15$ and $36=999999-279=999720$