Question

Find the smallest number that leaves the remainder 1 when divided by 2,3,4,5,6,7,8,9,10 but is divisible by 11

Answer 1

Heya user,

Clearly, such a no. is [ multiple of LCM of 2,3,4,5,6,7,8,9,10 ] + 1

Now, LCM[ 2,3,4,5,6,7,8,9,10 ] = 2520;

Hence, our req.d no. is 2520x + 1...

Now, since 11 divides our no., 11 | 2520x + 1

=> 11 | 2519x + x + 1 => 11 | 11*229x + x + 1 => 11 | x + 1

Hence, x = 10 is the smallest possible soln...
This, our smallest no. that Holds all such criteria is ----->

2520*10 + 1 = 25200 + 1 = 25201......☺