Question

Find the greatest number of five digits which become exactly divisible by $10,12,15$ and $18$ when $3769$ is added to it.

• A. $99819$
• B. $99911$
• C. $99900$
• D. $99111$

Answer 1

The correct option is B $99911$

$10=5\times 2$
$12=2\times 2\times 3$
$15=3\times 5$
$18=2\times 3\times 3$
L.C.M of $10,12,15,18=2\times 3\times 5\times 2\times 3=180$
The greatest five digit number $=99999$
According to the question, $99999+3769=103768$
When $103768÷180$, then reminder $=88$
$\therefore$ required number $=99999-88=99911$