Question

The smallest 4-digitnumber exactly divisible by $12,15,20and35$ is ...........

• A. $1,000$
• B. $1,160$
• C. $1,260$
• D. none of these

Answer 1

The correct option is C $1,260$

The smallest $4-digit=1000$
\Now L.C.M of 12, 15, 20 and 35
$L.C.M=2\times 2\times 3\times 5\times 7=420$
We divide 1000 by 420
420)1000(2
-840
160 -Remainder
$\therefore$ The least 4-digit number that is exactly divisible by 12,15,20 and 35
$=1000+(420-160)$
$=1000+260=1,260$