Question

Find the five digit smallest number which can be divided by be divided by $15,55$ and $99$ ?

Answer 1

Here, the prime factors of

$15=3\times 555=5\times 1199=3\times 3\times 11\therefore L.C.M.=3\times 3\times 5\times 11=495$

We know that the smallest five digit number is $10000$.

On dividing $10000$ by $L.C.M.495$ we get the remainder of $100$.

$\therefore$ The required smallest five digit number $=10000+(495-100)=10000+395=10395.$