Question

Find the smallest number which is completely divisible by 11, And those number divided by 3 , 4 , 6 and 9 remainder comes 2.

please , give appropriate answer with some explanation .

Answer 1

Take the LCM of 3, 4, 6 & 9
LCM = 2 * 2 * 3 * 3 = 36
i.e. 36 can divide 3,4,6,9 completely.
and 38 can divide 3, 4, 6, 9 leaving remainder 2.


Multiples of 36 = 36, 72, 108, 144.....
Numbers that can divide 3,4,6,9 leaving remainder 2 = 38, 74, 110, 146........


It is clear that the no. which is divisible by 11, and the no. divided by 3,4,6,9 leaving remainder 2, is the same.


So, answer is 110 ( from multiples of 36 ), because it is the smallest multiple of 11 which can divide 3,4,6,9 leaving remainder 2.

Hope it helps you !!!