The product of 45 and the counting number n is a perfect cube. find the least possible value for n.
PLS HELP.

The counting number n is 75 which when multiplied with 45 gives perfect cube.

Numbers which are the triple product of the exact number are known as perfect cubes.

In other words, we can say the value produced by multiplying a whole number by three times itself is a perfect cube.

A number that may be expressed as three times the product of another integer is also termed as a perfect cube.

It is given in the question that the product of 45 and the counting number n is a perfect cube
So, we have to find the counting number n

First of all we will factorise 45

45 = 5 × 9

After factorising we get,

45 = 3×3×5

For 45 to become perfect cube we have to multiply the factors with 3×5²

45 = 3×3×3×5×5×5

∴ 3×5² = 75

Hence , the counting number n is 75 which when multiplied with 45 gives perfect cube.

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