Finding the digits : Modular Arithmetic

Carmichael function says

(since $\lambda(2^2 5^2)=\text{lcm}(\lambda(2^2),\lambda(5^2))$ $=\text{lcm}(2,20)=20$ )

$3^{1234}\equiv 3^{1234\pmod {\lambda (100)}}\equiv 3^{14}\equiv \boxed{69}\pmod {100}$ .