Questions & Answers

Question

Answers

A) 100

B) 400

C) 900

D) 1024

Answer
Verified

As we know that we have to find the smallest square number which is exactly divisible by each of the numbers 6,9 and 15

So we take LCM (LOWEST COMMON FACTOR) by prime factorization method.

So LCM of 6,9,15

\[6 = 2 \times 3\]

$9 = 3 \times 3$

$15 = 3 \times 5$

From this LCM of 6,9,15 = $2 \times 3 \times 3 \times 5$

LCM of 6,9,15 = $90$

So we have $2 \times 3 \times 3 \times 5$ but this is not a perfect square

To make $2 \times 3 \times 3 \times 5$ as perfect square this we have to make equal pair of 2,3,5 as we see that 3 is in pair but 2 and 5 is not in pair so to making pair we have to multiply it by 2,5 so that it is perfect square.

So we multiply it by 2 and 5 we get

$2 \times 2 \times 3 \times 3 \times 5 \times 5$

So the required square number is $900$

So option C is the correct answer.

We can find LCM by using a division method so in this we have to multiply all the divisors to find LCM.