Question

With what smallest number should 15435 be divided to make it perfect cube

Answer 1

to make it perfect cube.find lcm and then divide by those no.which are not in group of 3.so we have to divide it by 45

Answer 2

The smallest number is 45, which after division makes 15435 as perfect cube.

Given:

• A number.
• 15435.

To find:

• With what smallest number should 15435 be divided to make it perfect cube.

Solution:

Concept to be used:

• Write prime factors of number.
• Remove the prime numbers which are not in power as 3.

Step 1:

Write prime factors of number.

$15435 = 3 \times 3 \times 5 \times 7 \times 7 \times 7$

or

$\bf 15435 = {3}^{2} \times 5 \times {7}^{3}$

Step 2:

Divide by 3²×5.

It has been clear that, the number can't be a perfect cube(when division is to be performed), until divided by 45.

So,

$45)15435(343 \\ 135 \\ - - - - \\ 193 \\ 180 \\ - - - - \\ 135 \\ 135 \\ - - - - \\ 0 \\ - - - -$

Now,

$\bf \sqrt[3]{343} = 7$

or

$\bf ( {7)}^{3} = 343$

Thus,

The smallest number is 45, which after division makes 15435 as perfect cube.

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