What is the least number which when divided by the numbers 3,5,6,8,10,and 12 leaves in each case a remainder 2, but when divided by 13 leaves no remainder is

By option verification ,

962 is divided by 3,5,6,8,10 and 12 leaves remainder 2, but when divided by 13 leaves no remainder

                     (or)

L.C.M of 3,5,6,8,10,12 is 120

$1\times 120+2=122$ is not divisible by 13

$2\times 120+2=242$ is not divisible by 13

$3\times 120+2=362$ is not divisible by 13

$4\times 120+2=482$ is not divisible by 13

$5\times 120+2=602$ is not divisible by 13

$6\times 120+2=722$ is not divisible by 13

$7\times 120+2=842$ is not divisible by 13

$8\times 120+2=962$  is divisible by 13