Of the options given, $$23\times 34$$, $$56\times 67$$ and $$67\times 78$$ are all not divisible by $$5$$, so may be discounted. Also $$34$$ is not divisible by $$4$$ and $$45$$ is odd, so $$34\times 45$$ may also be discounted as it is not divisible by $$4$$. The only other option is $$45\times 56$$. As a product of prime factors, $$45\times 56=2^{3}\times3^{2}\times5\times7$$, so it is clear that it is divisible by all of the integers from $$1$$ to $$10$$ inclusive. 
Which of the following is divisible by all of the integers from $$1$$ to $$10$$ inclusive? 
  - $$23\times34$$ 
  - $$34\times45$$ 
  - $$45\times56$$ 
  - $$56\times67$$ 
  - $$67\times78$$ 