What are the last three digits of the answer to the calculation below?  $$123\times 124\times 125\times 126\times 127$$ 
Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Applying the Properties of Dividing without Remainders->Maximum/Minimum Problems of Division without Remainders 
The product $$123 \times124\times125\times126 \times127$$ is a multiple of $$125$$; moreover, it also has a factor of $$2$$ three times, from $$124\left( 2\times 2\times 31 \right)$$ and from $$126\left( =2\times 63 \right)$$. Therefore it is a multiple of $$125 \times2\times2\times2= 1000$$, and so it must end in $$000$$. Alternatively, working from the options, it is easily seen that the product is a certainly an even multiple of $$5$$-so its unit digit is $$0$$. 