Question

Find least number which when divided by 6,7,8,9 and 10 leaves remainder 1

Answer 1

Find LCM ( 6,7,8,9,10 ) = 7560 which is divisible by all given digits. So, when we add 1 to 7560 and divided by given digits leaves remainder 1 .
i.e., 7560 + 1 = 7561 is the number which when divided by (6,7,8,9,10) leaves remainder 1.

Answer 2

6=2*3

7=1*7

8=2*2*2

9=3*3

10=2*5

So, the L.C.M of 6,7,8,9 and 10 is = (2*2*2*3*3*7)

                                                       = 504

So, the number is (504+1)

                             = 505