Question

find the smallest square number that is divisible by each of the numbers 18,15 and 20

Answer 1

First, we need to find the LCM of 18, 15 and 20.

$\begin{array}{r | l} 2 & 18,15,20 \\ \cline{2-2} 3 & 9,15,10 \\ \cline{2-2} & 3,5,2 \\ \end{array}$

LCM of 18, 15 and 20 is ⇒ $2\times 2\times 3\times 3 \times 5$

Now we pair the primes ⇒ $(2\times 2)\times (3\times 3) \times 5$

Since 5 doesn't have a pair, we need to multiply the LCM by 5.

$180\times 5 =900$

900 ⇒ $2\times 2\times 3\times 3 \times 5\times 5$

Since all the numbers have pairs, 900 is the smallest number that is divisible by 18, 15 and 20.

Additional Information :)

What is a square number?

The result of multiplying an integer by itself is known as a square number.

How to pronounce a squared number?

For example ⇒ $5^2$

We pronounce it as ⇒ "5 square" or "5 raised to the power 2"

What is the result if a negative number is squared?

The result will be positive if a negative number is squared.