Question

The largest natural number by which the product of three consecutive even natural numbers is always divisible , is ______ .

• A. $16$
• B. $24$
• C. $48$
• D. $96$

Answer 1

Answer: (C)

$48$

Let three consecutive even numbers be $2n,2n+2,2n+4$

product$=2n(2n+2)(2n+4)$

If $n=1,$

product $=2\left(4\right)\left(6\right)=48$

If $n=3,$

product $=6\times 8\times 10=480$

Which is the least number always divisible by $48$