Question

find the least number which when divided by 6 7 8 9 and 10 leaves 1 2 3 4 and 5 as remainders respectively but when divided by 19 leaves no remainder?

Answer 1

Lcm of (6,7,8,9,12) =504

Remainder is 1

So Number is in the format of 504K+1

Let K be 1

= 504 (1) +1

= 505

Or one could evem say that let K be 0

= 504 (0)+1

= 1