How many numbers between 400 and 800 are divisible by 4, 5 and 6 ?

L.C.M. of (4,5,6) = 60

Numbers between 400 and 800 that are divisible by 60 are : 420, 480, ......., 780

The above series is an arithmetic progression with first term $$=a=420$$, common difference $$=d=60$$ and last term $$=l=780$$

Let number of terms be $$n$$

Thus, last term of an A.P. = $$l=a+(n-1)d$$

=> $$420+(n-1)\times(60)=780$$

=> $$(n-1)\times(60)=780-420=360$$

=> $$(n-1)=\frac{360}{60}=6$$

=> $$n=6+1=7$$

$$\therefore$$ Numbers between 400 and 800 are divisible by 4, 5 and 6 = 7

=> Ans - (A)