Question

What is the smallest number which when divided by 20, 25, 35, 40 leaves a remainder of 14, 19, 29 and 34 respectively?

• A. 1406
• B. 1606
• C. 1394
• D. 1404

Answer 1

The correct option is C 1394


$\therefore$ L.C.M = 5 $\times$ 2 $\times$ 2 $\times$ 5 $\times$ 7 $\times$ 2
= 1400
Given, the smallest number which when divided by 20, 25, 35, 40 leaves a remainder of 14, 19, 29 and 34 respectively.
$\because$ 20 - 14 = 25 - 19 = 35 - 29 = 40 - 34 = 6
Here, the difference is equal. So, 6 should be subtracted from the LCM to get the number.
$\therefore$ The smallest number $=L.C.M-6$
$=1400-6=1394$