Question

Find the smallest number by which \[135\] must be divided, so that the quotient is a perfect cube.
A. $3$
B.$5$
C.$9$
D.$15$

Answer 1

Hint: We will do prime factorization of 135.Further we will divide 135 to a number, that number is not in triplet form. Then we will convert 135 into a perfect cube.


Complete step by step solution:
Here the given number is $135$
We will use prime factorization method

$3$	$135$
$3$	$45$
$3$	$15$
$5$	$5$
	$1$

$135 = 3 \times 3 \times 3 \times 5$
$135 = {3^3} \times 5$
Here, one $5$ is left which does not form a triplet
If we divide $135$ by $5$, then it will become a perfect cube.
So, $\dfrac{{135}}{5} = {3^3}$
$27 = {3^3}$
Hence, the smallest number by which $135$ should be divided to make it a perfect cube is $5$.

Note: In these types of questions usually students get puzzled whether to find HCF or LCM. We note that words like larger, highest etc. are keywords mentioned in the question and they give us ideas to find HCF whereas words like smallest, lowest, least etc. give us direction to find the LCM.