Question

The least number which when divided by $6,9,12,15,18$ leaves the same remainder $5$ in each case, is

Answer 1

To find the least number which when divided by $6,9,12,15,18$ leaves the same remainder $5$ in each case, we have to find the $LCMof6,9,12,15,18andadd5$to it.

By prime factorisation method

$6=2\times 3$

$9=3\times 3$

$12=2\times 2\times 3$

$15=3\times 5$

$18=2\times 3\times 3$

The $LCMof6,9,12,15,18=2\times 2\times 3\times 3\times 5=180$.

Now, $180+5=185$

Hence, the least number which when divided by $6,9,12,15,18$ leaves the same remainder $5$ in each case, is $185.$