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

Given:

There are three consecutive even numbers.

Calculation:

Let the numbers would be 2n, 2n + 2, 2n + 4.

Product would be 8n(n + 1)(n + 2).

Now clearly, the number is divisible by 8 and at least one more factor n, n + 1, n + 2 is even and divisible by 2 and in the three consecutive number, at least one is divisible by 3 .

So in this case the largest divisor of the product would be 8 x 3 x 2 = 48

∴ The number by which the product of three consecutive even numbers would be exactly divisible is 48.

In three consecutive numbers there will be two even numbers one a 8 multiple, another number which is  2 multiple and another number which is a 3 multiple.

So it will be divisible by 8 x 3 x 2 = 48.

∴ The number by which the product of three consecutive even numbers would be exactly divisible is 48.