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Let the five natural numbers be(x-2),(x-1) ,x, (x+1),(x+2)
If it is a multiple of 3 then..
We can write,
Five natural numbers are 3(x-2),3(x-1),3x,3(x+1),3(x+2)
If we take cube of any natural number,
Suppose,
{3(x-2)}³
=27(x-2)³___which is a multiple of 27__
Similarly,
{3(x-1)}³ = 27 (x-1)³
{3x}³ = 27 x³
{3(x+1)}³ = 27(x+1)³
{3(x+2)}³ = 27(x+2)³
By this we can see that any cube of the natural number, which is multiple of 3, is the multiple of 27.__(verified)__
Hope this is ur required answer
Proud to help you
If it is a multiple of 3 then..
We can write,
Five natural numbers are 3(x-2),3(x-1),3x,3(x+1),3(x+2)
If we take cube of any natural number,
Suppose,
{3(x-2)}³
=27(x-2)³___which is a multiple of 27__
Similarly,
{3(x-1)}³ = 27 (x-1)³
{3x}³ = 27 x³
{3(x+1)}³ = 27(x+1)³
{3(x+2)}³ = 27(x+2)³
By this we can see that any cube of the natural number, which is multiple of 3, is the multiple of 27.__(verified)__
Hope this is ur required answer
Proud to help you
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