find L.C.M. of 20,35,42 using common division method . hence find the least 4 digit no. which is divisible by 20,35,42leaving a remainder of 6 in each case.

L.C.M. of 20, 35 and 42 is given by;
$$\begin{gathered} 2 \left|20, 35, 42\right| \\ \overline{ 5 \left|10, 35, 21\right|} \\ \overline{ 7\left|2, 7, 21\right|} \\ \overline{ 2, 1, 3} \\ \mathrm{L}.\mathrm{C}.\mathrm{M}. \mathrm{of} 20, 35 \mathrm{and} 42 = 2\times 5\times 7\times 2\times 3 = 420 \end{gathered}$$
The least four digit number is 1000.
$$\begin{gathered} 420\left)1000\right(2 \\ 840 \\ \overline{ 160} \end{gathered}$$
Subtracting 160 from 420 we get; 420- 160 = 260
So the smallest four digit number which is divisible by 20, 35 and 42 is (1000 + 260) = 1260
And therefore the smallest four digit number which is divisible by 20, 35 and 42 leaving a remainder 6 in each case is 1260 + 6 = 1266