The least number which when divided by $15,27,35$  and $\text{42}$ leaves a remainder $\text{'}7\text{'}$  in each case is

The L.C.M. of $15,27,35$  and $\text{42}$  $=3\times 5\times 7\times 1\times 9\times 1\times 2$

$=1890$

leaves a remainder $\text{'}7\text{'}$  in each case $=1890+7$

$=1897$